Preprints
[129] Holden, Helge; Risebro, Nils Henrik: The continuum limit of higher-order Follow-the-Leader models. Preprint, submitted. [arXiv]
[128] Aggarwal, Aekta; Holden, Helge; Vaidya, Ganesh: Systems of nonlocal balance laws for dense multilane vehicular traffic. Preprint, submitted. [arXiv]
Publications in international, refereed journals
[130] Hanche-Olsen, Harald; Holden, Helge: The Aubin-Lions-Dubinskii theorems on compactness in Bochner spaces. To appear in Pure and Applied Functional Analysis. [arXiv]
[127] Aggarwal, Aekta; Holden, Helge; Vaidya, Ganesh: Well-posedness and error estimates for coupled systems of nonlocal conservation laws. IMA Journal of Numerical Analysis, Jan 2024. [journal] [arXiv]
[126] Aggarwal, Aekta; Holden, Helge; Vaidya, Ganesh: On the accuracy of the finite volume approximations to nonlocal conservation laws. Numerische Mathematik 156 (2024) 237-271. [journal] [arXiv]
[125] Galimberti, Luca; Holden, Helge; Karlsen, Kenneth H.; Pang, Peter H.C.: Global existence of dissipative solutions to the Camassa–Holm equation with transport noise. Journal of Differential Equations 387 (2024) 1-103. [journal] [arXiv]
[124] Holden, Helge; Karlsen, Kenneth H.; Pang, Peter H.C.: Global well-posedness of the viscous Camassa–Holm equation with gradient noise. Discrete and Continuous Dynamical Systems 43 (2023) 568-618 [journal] [arXiv]
[123] Carrillo, José A.; Holden, Helge; Solem, Susanne: Noise-driven bifurcations in a neural field system modelling networks of grid cells. Journal of Mathematical Biology 85, Article 42, 2022 [journal] [arXiv]
[122] Grunert, Katrin; Holden, Helge: Uniqueness of conservative solutions for the Hunter–Saxton equation. Research in the Mathematical Sciences 9, Article 19, 2022 [journal] [arXiv]
[121] Holden, Helge; Karlsen, Kenneth H.; Pang, Peter H.C.: Strong solutions of a stochastic differential equation with irregular random drift. Stochastic Processes and their Applications 150 Aug 2022, 655-677 [journal] [arXiv]
[120] Grotschel, Martin; Hanche-Olsen, Harald; Holden, Helge; Krystek, Michael P.: On angular measures in axiomatic Euclidean planar geometry. Measurement Science Review, Vol. 22, no 4, (2022) 152-159 [journal] [arXiv]
[119] Grunert, Katrin; Holden, Helge; Jacobsen, Espen R.; Stenseth, Nils Christian: Evolutionary stable strategies in stable and periodically fluctuating populations: the Rosenzweig–MacArthur predator-prey model. Proceedings of the National Academy of Sciences of the United States of America, (2021) Vol. 118 No. 4 e2017463118. [journal]
Commentary: K. Sigmund, R.D. Holt: Toward ecoevolutionary dynamics. loc.sit. (2021) Vol 118 No 9 e2100200118. [journal]
Letter: A. Best, B. Ashby: Evolutionarily stable strategies are well studied in periodically fluctuating population. loc.sit. (2021) Vol 118 (18) e2102001118. [journal]
Reply: The concept of evolutionarily stable strategies (ESS) helps link ecology and evolution. loc.sit. (2021) Vol 118 No 18 e2102861118. [journal]
[118] Coclite, Giuseppe M.; Holden, Helge; Risebro, Nils Henrik: Singular diffusion with Neumann boundary conditions. Nonlinearity 34 (2021), 1633– 1662. [journal] [arXiv]
[117] Holden, Helge; Karlsen, Kenneth H.; Pang, Peter H.C.: The Hunter–Saxton equation with noise. Journal of Differential Equations 270 (2021), no 5, 725–786. [journal] [arXiv]
[116] Colombo, Rinaldo M.; Holden, Helge; Marcellini, Francesca: On the microscopic modeling of vehicular traffic on general networks. SIAM J. Appl. Math. 80 (2020), no. 3, 1377–1391. [journal] [arXiv]
[115] Carrillo, José A.; Grunert, Katrin; Holden, Helge: A Lipschitz metric for the Camassa-Holm equation. Forum Math. Sigma 8 (2020), Paper No. e27, 292 pp. [journal] [arXiv]
[114] Holden, Helge; Risebro, Nils Henrik: Models for dense multilane vehicular traffic. SIAM J. Math. Anal. 51 (2019), no. 5, 3694–3713. [journal] [arXiv]
[113 ] Holden, Helge; Risebro, Nils Henrik: Follow-the-leader models can be viewed as a numerical approximation to the Lighthill-Whitham-Richards model for traffic flow. Netw. Heterog. Media 13 (2018), no. 3, 409–421. [journal] [arXiv]
[112] Hanche-Olsen, Harald; Holden, Helge; Malinnikova, Eugenia: An improvement of the Kolmogorov-Riesz compactness theorem. Expo. Math. 37 (2019), no. 1, 84–91. [journal] [arXiv]
[111] Holden, Helge; Risebro, Nils Henrik: The continuum limit of Follow-the-Leader models—a short proof. Discrete Contin. Dyn. Syst. 38 (2018), no. 2, 715–722. [journal] [arXiv]
[110] Carrillo, José Antonio; Grunert, Katrin; Holden, Helge: A Lipschitz metric for the Hunter-Saxton equation. Comm. Partial Differential Equations 44 (2019), no. 4, 309–334. [journal] [arXiv]
[109] Behrndt, Jussi; Gesztesy, Fritz; Holden, Helge; Nichols, Roger: Dirichlet-to-Neumann maps, abstract Weyl-Titchmarsh M-functions, and a generalized index of unbounded meromorphic operator-valued functions. J. Differential Equations 261 (2016), no. 6, 3551–3587. [journal] [arXiv]
[108] Eckhardt, Jonathan; Gesztesy, Fritz; Holden, Helge; Kostenko, Aleksey; Teschl, Gerald: Real-valued algebro-geometric solutions of the two-component Camassa-Holm hierarchy. Ann. Inst. Fourier (Grenoble) 67 (2017), no. 3, 1185–1230. [journal] [arXiv]
[107] Colombo, Rinaldo M.; Holden, Helge: Isentropic fluid dynamics in a curved pipe. Z. Angew. Math. Phys. 67 (2016), no. 5, Art. 131, 10 pp. [journal] [arXiv]
[106] Dutta, R.; Holden, H.; Koley, U.; Risebro, N. H.: Operator splitting for the Benjamin-Ono equation. J. Differential Equations 259 (2015), no. 11, 6694–6717. [journal] [arXiv]
[105] Grunert, Katrin; Holden, Helge: The general peakon-antipeakon solution for the Camassa-Holm equation. J. Hyperbolic Differ. Equ. 13 (2016), no. 2, 353–380. [journal] [arXiv]
[104] Dutta, Rajib; Holden, Helge; Koley, Ujjwal; Risebro, Nils Henrik: Convergence of finite difference schemes for the Benjamin-Ono equation. Numer. Math. 134 (2016), no. 2, 249–274. [journal] [arXiv]
[103] Colombo, Rinaldo M.; Holden, Helge: On the Braess paradox with nonlinear dynamics and control theory. J. Optim. Theory Appl. 168 (2016), no. 1, 216–230. [journal] [arXiv]
[102] Gesztesy, Fritz; Holden, Helge; Nichols, Roger: On factorizations of analytic operator-valued functions and eigenvalue multiplicity questions. Integral Equations Operator Theory 82 (2015), no. 1, 61–94. [ journal] [arXiv]. Erratum ibid. 85 (2016), no. 2, 301–302. [journal]
[101] Grunert, Katrin; Holden, Helge; Raynaud, Xavier: A continuous interpolation between conservative and dissipative solutions for the two-component Camassa-Holm system. Forum Math. Sigma 3 (2015), Paper No. e1, 73 pp. [journal] [arXiv]
[100] Grunert, Katrin; Holden, Helge; Raynaud, Xavier: Global dissipative solutions of the two-component Camassa-Holm system for initial data with nonvanishing asymptotics. Nonlinear Anal. Real World Appl. 17 (2014), 203–244. [journal] [arXiv]
[99] Holden, Helge; Priuli, Fabio Simone; Risebro, Nils Henrik: On an inverse problem for scalar conservation laws. Inverse Problems 30 (2014), no. 3, 035015, 35 pp. [journal] [arXiv]
[98] Holden, Helge; Koley, Ujjwal; Risebro, Nils Henrik: Convergence of a fully discrete finite difference scheme for the Korteweg–de Vries equation. IMA J. Numer. Anal. 35 (2015), no. 3, 1047–1077. [journal] [arXiv]
[97] Holden, Helge; Karlsen, Kenneth H.; Karper, Trygve K.: Operator splitting for well-posed active scalar equations. SIAM J. Math. Anal. 45 (2013), no. 1, 152–180. [journal] [arXiv]
[96] Grunert, Katrin; Holden, Helge; Raynaud, Xavier: Global solutions for the two-component Camassa-Holm system. Comm. Partial Differential Equations 37 (2012), no. 12, 2245–2271. [journal] [arXiv]
[95] Grunert, Katrin; Holden, Helge; Raynaud, Xavier: Global conservative solutions to the Camassa-Holm equation for initial data with nonvanishing asymptotics. Discrete Contin. Dyn. Syst. 32 (2012), no. 12, 4209–4227. [journal] [arXiv]
[94] Holden, Helge; Lubich, Christian; Risebro, Nils Henrik: Operator splitting for partial differential equations with Burgers nonlinearity. Math. Comp. 82 (2013), no. 281, 173–185. [journal] [arXiv]
[93] Holden, Helge; Karlsen, Kenneth H.; Karper, Trygve: Operator splitting for two-dimensional incompressible fluid equations. Math. Comp. 82 (2013), no. 282, 719–748. [journal] [arXiv]
[92] Gesztesy, Fritz; Goldstein, Jerome A.; Holden, Helge; Teschl, Gerald: Abstract wave equations and associated Dirac-type operators. Ann. Mat. Pura Appl. (4) 191 (2012), no. 4, 631–676. [journal] [arXiv]
[91] Grunert, Katrin; Holden, Helge; Raynaud, Xavier: Lipschitz metric for the Camassa-Holm equation on the line. Discrete Contin. Dyn. Syst. 33 (2013), no. 7, 2809–2827. [journal] [arXiv]
[90] Gesztesy, Fritz; Holden, Helge: The damped string problem revisited. J. Differential Equations 251 (2011), no. 4-5, 1086–1127. [journal] [arXiv]
[89] Frid, Hermano; Holden, Helge; Karlsen, Kenneth H.: L∞ solutions for a model of nonisothermal polytropic gas flow. SIAM J. Math. Anal. 43 (2011), no. 5, 2253–2274. [journal] [arXiv]
[88] Grunert, Katrin; Holden, Helge; Raynaud, Xavier: Lipschitz metric for the periodic Camassa-Holm equation. J. Differential Equations 250 (2011), no. 3, 1460–1492. [journal] [arXiv]
[87] Holden, Helge; Karlsen, Kenneth H.; Mitrovic, Darko; Panov, Evgueni Yu.: Strong compactness of approximate solutions to degenerate elliptic-hyperbolic equations with discontinuous flux function. Acta Math. Sci. Ser. B (Engl. Ed.) 29 (2009), no. 6, 1573–1612. [journal]
[86] Holden, Helge; Raynaud, Xavier: Global semigroup of conservative solutions of the nonlinear variational wave equation. Arch. Ration. Mech. Anal. 201 (2011), no. 3, 871–964. [journal] [arXiv]
[85] Holden, Helge; Karlsen, Kenneth H.; Risebro, Nils Henrik; Tao, Terence: Operator splitting for the KdV equation. Math. Comp. 80 (2011), no. 274, 821–846. [journal] [arXiv]
[84] Hanche-Olsen, Harald; Holden, Helge: The Kolmogorov-Riesz compactness theorem. Expo. Math. 28 (2010), no. 4, 385–394. [journal] [arXiv]. Addendum ibid. 34 (2016), no. 2, 243–245. [journal] [arXiv]
[83] Bressan, Alberto; Holden, Helge; Raynaud, Xavier: Lipschitz metric for the Hunter-Saxton equation. J. Math. Pures Appl. (9) 94 (2010), no. 1, 68–92. [journal] [arXiv]
[82] Holden, H.; Karlsen, K. H.; Mitrovic, D.: Zero diffusion-dispersion-smoothing limits for a scalar conservation law with discontinuous flux function. Int. J. Differ. Equ. 2009, Art. ID 279818, 33 pp. [journal]
[81] Ehrnström, Mats; Holden, Helge; Raynaud, Xavier: Symmetric waves are traveling waves. Int. Math. Res. Not. IMRN 2009, no. 24, 4578–4596. [journal] [arXiv]
[80] Holden, Helge; Risebro, Nils Henrik; Sande, Hilde: Front tracking for a model of immiscible gas flow with large data. BIT 50 (2010), no. 2, 331–376. [journal]
[79] Holden, H.; Raynaud, X.: Global dissipative multipeakon solutions of the Camassa-Holm equation. Comm. Partial Differential Equations 33 (2008), no. 10-12, 2040–2063. [journal]
[78] Coclite, Giuseppe Maria; Holden, Helge: Ground states of the Schrödinger-Maxwell system with Dirac mass: existence and asymptotics. Discrete Contin. Dyn. Syst. 27 (2010), no. 1, 117–132. [journal]
[77] Holden, Helge; Raynaud, Xavier: Dissipative solutions for the Camassa-Holm equation. Discrete Contin. Dyn. Syst. 24 (2009), no. 4, 1047–1112. [journal]
[76] Gesztesy, Fritz; Holden, Helge; Michor, Johanna; Teschl, Gerald: Local conservation laws and the Hamiltonian formalism for the Ablowitz-Ladik hierarchy. Stud. Appl. Math.120 (2008), no. 4, 361–423. [journal] [arXiv]
[75] Holden, Helge; Risebro, Nils Henrik; Sande, Hilde: The solution of the Cauchy problem with large data for a model of a mixture of gases. J. Hyperbolic Differ. Equ. 6 (2009), no. 1,25–106. [journal]
[74] Holden, H.; Karlsen, K. H.; Risebro, N. H.: A convergent finite-difference method for a nonlinear variational wave equation. IMA J. Numer. Anal. 29 (2009), no. 3, 539–572. [journal] [arXiv]
[73] Gesztesy, Fritz; Holden, Helge; Michor, Johanna; Teschl, Gerald: The algebro-geometric initial value problem for the Ablowitz-Ladik hierarchy. Discrete Contin. Dyn. Syst. 26 (2010), no. 1, 151–196. [journal] [arXiv]
[ 72] Gesztesy, Fritz; Holden, Helge; Michor, Johanna; Teschl, Gerald: Algebro-geometric finite-band solutions of the Ablowitz-Ladik hierarchy. Int. Math. Res. Not. IMRN 2007, no. 20, Art. ID rnm082, 55 pp. [journal] [arXiv]
[71] Holden, Helge; Holden, Lars: Optimal rebalancing of portfolios with transaction costs. Stochastics 85 (2013), no. 3, 371–394. [journal]
[70] Coclite, G. M.; Holden, H.; Karlsen, K. H.: Well-posedness of higher-order Camassa-Holm equations. J. Differential Equations 246 (2009), no. 3, 929–963. [journal]
[69] Holden, Helge; Raynaud, Xavier: Periodic conservative solutions of the Camassa-Holm equation. Ann. Inst. Fourier (Grenoble) 58 (2008), no. 3, 945–988. [journal]
[68] Gesztesy, Fritz; Holden, Helge: Local conservation laws and the Hamiltonian formalism for the Toda hierarchy revisited. Skr. K. Nor. Vidensk. Selsk. 2006, no. 3, 30 pp. [paper] [arXiv]
[67] Holden, Helge; Raynaud, Xavier: Global conservative solutions of the generalized hyperelastic-rod wave equation. J. Differential Equations 233 (2007), no. 2, 448–484. [journal]
[66] Holden, Helge; Raynaud, Xavier: Global conservative multipeakon solutions of the Camassa-Holm equation. J. Hyperbolic Differ. Equ. 4 (2007), no. 1, 39–64. [journal]
[65] Gesztesy, Fritz; Holden, Helge; Teschl, Gerald: The algebro-geometric Toda hierarchy initial value problem for complex-valued initial data. Rev. Mat. Iberoam. 24 (2008), no. 1,117–182. [journal] [arXiv]
[64] Holden, Helge; Raynaud, Xavier: Global conservative solutions of the Camassa-Holm equation—a Lagrangian point of view. Comm. Partial Differential Equations 32 (2007), no. 10-12,1511–1549. [journal]
[63] Coclite, G. M.; Holden, H.: The Schrödinger-Maxwell system with Dirac mass. Ann. Inst. H. Poincaré Anal. Non Linéaire 24 (2007), no. 5, 773–793. [journal] . Erratum ibid. 25 (2008), no. 4, 833–836. [journal]
[62] Holden, H.; Karlsen, K. H.; Risebro, N. H.: Convergent difference schemes for the Hunter-Saxton equation. Math. Comp. 76 (2007), no. 258, 699–744. [journal]
[61] Holden, Helge; Raynaud, Xavier: A convergent numerical scheme for the Camassa-Holm equation based on multipeakons. Discrete Contin. Dyn. Syst. 14 (2006), no. 3, 505–523. [journal]
[60] Coclite, G. M.; Holden, H.; Karlsen, K. H.: Global weak solutions to a generalized hyperelastic-rod wave equation. SIAM J. Math. Anal. 37 (2005), no. 4, 1044–1069. [journal]
[59] Coclite, Giuseppe Maria; Holden, Helge; Karlsen, Kenneth Hvistendahl: Wellposedness for a parabolic-elliptic system. Discrete Contin. Dyn. Syst. 13 (2005), no. 3, 659–682. [journal]
[58] Holden, Helge; Holden, Lars; Holden, Steinar: Contract adjustment under uncertainty. J. Econom. Dynam. Control 34 (2010), no. 4, 657–680. [journal]
[57] Holden, Helge; Raynaud, Xavier: Convergence of a finite difference scheme for the Camassa-Holm equation. SIAM J. Numer. Anal. 44 (2006), no. 4, 1655–1680. [journal]
[56] Geronimo, Jeffrey S.; Gesztesy, Fritz; Holden, Helge: Algebro-geometric solutions of the Baxter-Szegő difference equation. Comm. Math. Phys. 258 (2005), no. 1, 149–177. [journal] [arXiv]
[55] Coclite, Giuseppe Maria; Holden, Helge: Stability of solutions of quasilinear parabolic equations. J. Math. Anal. Appl. 308 (2005), no. 1, 221–239. [journal] [arXiv]
[54] Cascaval, Radu C.; Gesztesy, Fritz; Holden, Helge; Latushkin, Yuri: Spectral analysis of Darboux transformations for the focusing NLS hierarchy. J. Anal. Math. 93 (2004), 139–197. [journal] [arXiv]
[53] Holden, Helge; Karlsen, Kenneth H.; Risebro, Nils H.: On uniqueness and existence of entropy solutions of weakly coupled systems of nonlinear degenerate parabolic equations. Electron. J. Differential Equations 2003, No. 46, 31 pp. [paper]
[52] Eilbeck, J. C.; Enolskii, V. Z.; Holden, H.: The hyperelliptic ζ-function and the integrable massive Thirring model. R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci.459 (2003), no. 2035, 1581–1610. [journal]
[51] Gesztesy, Fritz; Holden, Helge: Real-valued algebro-geometric solutions of the Camassa-Holm hierarchy. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 366 (2008), no. 1867, 1025–1054. [journal] [arXiv]
[50] Gesztesy, Fritz; Holden, Helge: Algebro-geometric solutions of the Camassa-Holm hierarchy. Rev. Mat. Iberoamericana 19 (2003), no. 1, 73–142. [journal] [arXiv]
[49] Holden, Helge; Karlsen, Kenneth H.; Lie, Knut-Andreas: Operator splitting methods for degenerate convection-diffusion equations II: Numerical examples with emphasis on reservoir simulation and sedimentation. Computational Geosciences 4 (2000) 287–322. [journal]
[48] Hanche-Olsen, Harald; Holden, Helge; Risebro, Nils Henrik: The Riemann problem for an elastic string with a linear Hooke's law. Quart. Appl. Math. 60 (2002), no. 4, 695–705. [journal]
[47] Clark, Steve; Gesztesy, Fritz; Holden, Helge; Levitan, Boris M.: Borg-type theorems for matrix-valued Schrödinger operators. J. Differential Equations 167 (2000), no. 1, 181–210. [journal] [arXiv]
[46] Gesztesy, Fritz; Holden, Helge: Darboux-type transformations and hyperelliptic curves. J. Reine Angew. Math. 527 (2000), 151–183. [journal] [arXiv]
[45] Gesztesy, Fritz; Holden, Helge: The classical Boussinesq hierarchy revisited. Skr. K. Nor. Vidensk. Selsk. 2000, no. 1, 15 pp. [paper] [arXiv]
[44] Holden, Helge; Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik: Operator splitting methods for generalized Korteweg-de Vries equations. J. Comput. Phys. 153 (1999), no. 1,203–222. [journal]
[43] Gesztesy, Fritz; Holden, Helge: Dubrovin equations and integrable systems on hyperelliptic curves. Math. Scand. 91 (2002), no. 1, 91–126. [journal] [arXiv]
[42] Holdahl, Runar; Holden, Helge; Lie, Knut-Andreas: Unconditionally stable splitting methods for the shallow water equations. BIT 39 (1999), no. 3, 451–472. [journal]
[41] Holden, Helge; Lie, Knut-Andreas; Risebro, Nils Henrik: An unconditionally stable method for the Euler equations. J. Comput. Phys. 150 (1999), no. 1, 76–96. [journal]
[40] Holden, Helge; Risebro, Nils Henrik: Riemann problems with a kink. SIAM J. Math. Anal. 30 (1999), no. 3, 497–515. [journal]
[39] Gesztesy, F.; Holden, H.; Simon, B.; Zhao, Z.: A trace formula for multidimensional Schrödinger operators. J. Funct. Anal. 141 (1996), no. 2, 449–465. [journal]
[38] Holden, Helge; Hu, Yaozhong: Finite difference approximation of the pressure equation for fluid flow in a stochastic medium—a probabilistic approach. Comm. Partial Differential Equations 21 (1996), no. 9-10, 1367–1388. [journal]
[37] Bulla, W.; Gesztesy, F.; Holden, H.; Teschl, G.: Algebro-geometric quasi-periodic finite-gap solutions of the Toda and Kac-van Moerbeke hierarchies. Mem. Amer. Math. Soc. 135 (1998), no. 641, x+79 pp. [journal] [arXiv]
[36] Holden, H.; Risebro, N. H.: Conservation laws with a random source. Appl. Math. Optim. 36 (1997), no. 2, 229–241. [journal]
[35] Gesztesy, F.; Holden, H.; Simon, B.; Zhao, Z.: Higher order trace relations for Schrödinger operators. Rev. Math. Phys. 7 (1995), no. 6, 893–922. [journal]
[34] Gesztesy, F.; Holden, H.; Simon, B.: Absolute summability of the trace relation for certain Schrödinger operators. Comm. Math. Phys. 168 (1995), no. 1, 137–161. [journal]
[33] Holden, Helge; Risebro, Nils Henrik; Tveito, Aslak: Maximum principles for a class of conservation laws. SIAM J. Appl. Math. 55 (1995), no. 3, 651–661. [journal]
[32] Holden, H.; Lindstrøm, T.; Øksendal, B.; Ubøe, J.; Zhang, T.-S.: The pressure equation for fluid flow in a stochastic medium. Potential Anal. 4 (1995), no. 6, 655–674. [journal]
[31] Holden, Helge; Risebro, Nils Henrik: A mathematical model of traffic flow on a network of unidirectional roads. SIAM J. Math. Anal. 26 (1995), no. 4, 999–1017. [journal]
[30] Gesztesy, F.; Holden, H.: Trace formulas and conservation laws for nonlinear evolution equations. Rev. Math. Phys. 6 (1994), no. 1, 51–95. [journal]. Errata: ibid.. 6 (1994), no. 4, 673. [journal]
[29] Gesztesy, F.; Holden, H.; Simon, B.; Zhao, Z.: Trace formulae and inverse spectral theory for Schrödinger operators. Bull. Amer. Math. Soc. (N.S.) 29 (1993), no. 2, 250–255. [journal] [arXiv]
[28] Holden, H.; Lindstrøm, T.; Øksendal, B.; Ubøe, J.; Zhang, T.-S.: The Burgers equation with a noisy force and the stochastic heat equation. Comm. Partial Differential Equations 19 (1994), no. 1-2, 119–141. [journal]
[27] Albeverio, S.; Gesztesy, F.; Holden, H.: Comments on a recent note on the Schrödinger equation with a δ′-interaction. J. Phys. A 26 (1993), no. 15, 3903–3904. [journal]
[26] Bratvedt, Frode; Bratvedt, Kyrre; Buchholz, Christian F.; Gimse, Tore; Holden, Helge; Holden, Lars; Risebro, Nils Henrik.; FRONTLINE and FRONTSIM: two full scale, two-phase, black oil reservoir simulators based on front tracking. Surveys Math. Indust. 3 (1993), no. 3, 185–215. [article]
[25] Holden, Helge; Lindstrøm, Tom; Øksendal, Bernt; Ubøe, Jan: Discrete Wick calculus and stochastic functional equations. Potential Anal. 1 (1992), no. 3, 291–306. [journal]
[24] Holden, Helge; Lindstrøm, Tom; Øksendal, Bernt; Ubøe, Jan; Zhang, Tu Sheng: Stochastic boundary value problems: a white noise functional approach. Probab. Theory Related Fields 95 (1993), no. 3, 391–419. [journal]
[23] Holden, Helge; Risebro, Nils Henrik: A method of fractional steps for scalar conservation laws without the CFL condition. Math. Comp. 60 (1993), no. 201, 221–232. [journal]
[22] Gesztesy, F.; Holden, H.; Simon, B.; Zhao, Z.: On the Toda and Kac-van Moerbeke systems. Trans. Amer. Math. Soc. 339 (1993), no. 2, 849–868. [journal]
[21] Holden, Helge; Risebro, Nils Henrik: Stochastic properties of the scalar Buckley-Leverett equation. SIAM J. Appl. Math. 51 (1991), no. 5, 1472–1488. [journal]
[20] Gesztesy, F.; Holden, H.; Saab, E.; Simon, B.: Explicit construction of solutions of the modified Kadomtsev-Petviashvili equation. J. Funct. Anal. 98 (1991), no. 1, 211–228. [journal]
[19] Bratvedt, F.; Bratvedt, K.; Buchholz, C.F.; Holden, H.; Holden, L.; Risebro, N.H.: A new front-tracking method for reservoir simulation. SPE Reservoir Engineering 7 (1992) 107–116. [journal]
[18] Albeverio, S.; Høegh-Krohn, R.; Holden, H.; Kolsrud, T.: Construction of quantized Higgs-like fields in two dimensions. Phys. Lett. B 222 (1989), no. 2, 263–268. [journal]
[17] Gesztesy, F.; Gurarie, D.; Holden, H.; Klaus, M.; Sadun, L.; Simon, B.; Vogl, P.: Trapping and cascading of eigenvalues in the large coupling limit. Comm. Math. Phys. 118 (1988), no. 4, 597–634. [journal]
[16] Albeverio, Sergio; Holden, Helge; Høegh-Krohn, Raphael; Kolsrud, Torbjörn: Representation and construction of multiplicative noise. J. Funct. Anal. 87 (1989), no. 2, 250–272. [journal]
[15] Figari, R.; Holden, H.; Teta, A.: A law of large numbers and a central limit theorem for the Schrödinger operator with zero-range potentials. J. Statist. Phys. 51 (1988), no. 1-2,205–214. [journal]
[14] Holden, H.; Holden, L.; Høegh-Krohn, R.: A numerical method for first order nonlinear scalar conservation laws in one dimension. Comput. Math. Appl. 15 (1988), no. 6-8, 595–602. [journal]
[13] Gesztesy, F.; Holden, H.: A new class of solvable models in quantum mechanics describing point interactions on the line. J. Phys. A 20 (1987), no. 15, 5157–5177. [journal]
[12] Holden, Helge: On the Riemann problem for a prototype of a mixed type conservation law. Comm. Pure Appl. Math. 40 (1987), no. 2, 229–264. [journal]
[11] Gesztesy, F.; Holden, H.; Kirsch, W.: On energy gaps in a new type of analytically solvable model in quantum mechanics. J. Math. Anal. Appl. 134 (1988), no. 1, 9–29. [journal]
[10] Albeverio, Sergio; Høegh-Krohn, Raphael; Holden, Helge: Stochastic multiplicative measures, generalized Markov semigroups, and group-valued stochastic processes and fields. J. Funct. Anal. 78 (1988), no. 1, 154–184. [journal]
[9] Albeverio, S.; Gesztesy, F.; Høegh-Krohn, R.; Holden, H.: Point interactions in two dimensions: basic properties, approximations and applications to solid state physics. J. Reine Angew. Math. 380 (1987), 87–107. [journal]
[8] Gesztesy, F.; Holden, H.: A unified approach to eigenvalues and resonances of Schrödinger operators using Fredholm determinants. J. Math. Anal. Appl. 123 (1987), no. 1, 181–198. [journal]. Addendum: ibid. 132 (1988), no. 1, 309. [journal]
[7] Holden, Helge: On coupling constant thresholds in two dimensions. J. Operator Theory 14 (1985), no. 2, 263–276. [journal]
[6] Høegh-Krohn, Raphael; Holden, Helge; Johannesen, Steinar; Wentzel-Larsen, Tore: The Fermi surface for point interactions. J. Math. Phys. 27 (1986), no. 1, 385–405. [journal]
[5] Holden, H.; Høegh-Krohn, R.; Mebkhout, M.: The short-range expansion for multiple well scattering theory. J. Math. Phys. 26 (1985), no. 1, 145–151. [journal]
[4] Holden, Helge; Høegh-Krohn, Raphael; Johannesen, Steinar: The short-range expansion in solid state physics. Ann. Inst. H. Poincaré Phys. Théor. 41 (1984), no. 4, 335–362. [journal]
[3] Martinelli, Fabio; Holden, Helge: On absence of diffusion near the bottom of the spectrum for a random Schrödinger operator on L2(Rν). Comm. Math. Phys. 93 (1984), no. 2, 197–217. [journal]
[2] Holden, Helge; Høegh-Krohn, Raphael; Johannesen, Steinar: The short range expansion. Adv. in Appl. Math. 4 (1983), no. 4, 402–421. [journal]
[1] Høegh-Krohn, Raphael; Holden, Helge; Martinelli, Fabio: The spectrum of defect periodic point interactions. Lett. Math. Phys. 7 (1983), no. 3, 221–228. [journal]
Publications in proceedings of conferences
[54] Holden, Helge: IMU Status Report. Proceedings of the International Congress of Mathematicians 2018 (ICM 2018). Volume 1. [book]
[53] Grasmair, Markus; Grunert, Katrin; Holden, Helge: On the equivalence of Eulerian and Lagrangian variables for the two-component Camassa-Holm system. Current Research in Nonlinear Analysis: In Honor of Haim Brezis and Louis Nirenberg, 157–201, Springer Optim. Appl., 135, Springer, Cham, 2018. [book] [arXiv]
[52] Holden, Helge: Burgers meets Braess. Oberwolfach Reports, vol. 13, issue 2, pp. 1715–1717, 2016. [article]
[51] Behrndt, Jussi; Gesztesy, Fritz; Holden, Helge; Nichols, Roger: On the index of meromorphic operator-valued functions and some applications. Functional analysis and operator theory for quantum physics, 95–127, EMS Ser. Congr. Rep., Eur. Math. Soc., Zürich, 2017. [book] [article]
[50] Grunert, Katrin; Holden, Helge; Raynaud, Xavier: Lipschitz metric for the two-component Camassa-Holm system. Hyperbolic problems: theory, numerics, applications, 193–207, AIMS Ser. Appl. Math., 8, Am. Inst. Math. Sci. (AIMS), Springfield, MO, 2014. [book] [arXiv]
[49] Grunert, Katrin; Holden, Helge; Raynaud, Xavier: Periodic conservative solutions for the two-component Camassa-Holm system. Spectral analysis, differential equations and mathematical physics: a festschrift in honor of Fritz Gesztesy's 60th birthday, 165–182, Proc. Sympos. Pure Math., 87, Amer. Math. Soc., Providence, RI, 2013. [book] [arXiv]
[48] Holden, Helge; Risebro, Nils Henrik; Sande, Hilde: Convergence of front tracking and the Glimm scheme for a model of the flow of immiscible gases. Hyperbolic problems: theory, numerics and applications, 653–662, Proc. Sympos. Appl. Math., 67, Part 2, Amer. Math. Soc., Providence, RI, 2009. [book] [article]
[47] Gesztesy, Fritz; Holden, Helge; Michor, Johanna; Teschl, Gerald: The Ablowitz-Ladik hierarchy revisited. Methods of spectral analysis in mathematical physics, 139–190, Oper. Theory Adv. Appl., 186, Birkhäuser Verlag, Basel, 2009. [book] [arXiv]
[46] Holden, H.; Raynaud, X.: A numerical scheme based on multipeakons for conservative solutions of the Camassa-Holm equation. Hyperbolic problems: theory, numerics, applications, 873–881, Springer, Berlin, 2008. [article]
[45] Coclite, G. M.; Holden, H.; Karlsen, K. H.: Global weak solutions for a shallow water equation. Hyperbolic problems: theory, numerics, applications, 389–396, Springer, Berlin, 2008. [article]
[44] Gesztesy, F.; Holden, H.: Algebro-geometric solutions of the KdV and Camassa–Holm equation. Oberwolfach Reports 1 (2004), pp. 275–279. [article]
[43] Holden, Helge: On the Camassa-Holm and Hunter-Saxton equations. European Congress of Mathematics, 173–200, Eur. Math. Soc., Zürich, 2005. [book]
[42] Enolskii, V. Z.; Gesztesy, F.; Holden, H.: The classical massive Thirring system revisited. Stochastic processes, physics and geometry: new interplays, I (Leipzig, 1999), 163–200, CMS Conf. Proc., 28, Amer. Math. Soc., Providence, RI, 2000. [book] [arXiv]
[41] Gesztesy, Fritz; Holden, Helge: A combined sine-Gordon and modified Korteweg-de Vries hierarchy and its algebro-geometric solutions. Differential equations and mathematical physics (Birmingham, AL, 1999), 133–173, AMS/IP Stud. Adv. Math., 16, Amer. Math. Soc., Providence, RI,2000. [book] [arXiv]
[40] Holden, Helge; Øksendal, Bernt: A white noise approach to stochastic Neumann boundary-value problems. Recent developments in infinite-dimensional analysis and quantum probability. Acta Appl. Math. 63 (2000), no. 1-3, 141–150. [journal]
[39] Holden, Helge; Karlsen, Kenneth Hvistendahl; Lie, Knut-Andreas; Risebro, Nils Henrik: Operator splitting for convection-dominated nonlinear partial differential equations. Godunov methods (Oxford, 1999), 469–475, Kluwer/Plenum, New York, 2001. [book]
[38] Holden, Helge; Karlsen, Kenneth Hvistendahl; Lie, Knut-Andreas: Operator splitting methods for degenerate convection-diffusion equations. I. Convergence and entropy estimates. Stochastic processes, physics and geometry: new interplays, II (Leipzig, 1999), 293–316, CMS Conf. Proc., 29, Amer. Math. Soc., Providence, RI, 2000. [book] [arXiv]
[37] Gesztesy, Fritz; Holden, Helge: The Cole-Hopf and Miura transformations revisited. Mathematical physics and stochastic analysis (Lisbon, 1998), 198–214, World Sci. Publ., River Edge, NJ, 2000. [book]
[36] Holden, Helge; Øksendal, Bernt: A white noise approach to stochastic differential equations driven by Wiener and Poisson processes. Nonlinear theory of generalized functions (Vienna, 1997), 293–313, Chapman & Hall/CRC Res. Notes Math., 401, Chapman & Hall/CRC, Boca Raton, FL,1999. [book]
[35] Holden, H.; Martinsen, T. With; Risebro, N.H.: Systems of conservation laws on networks — a model for traffic flow. Zeitschrift für Angewandte Mathematik und Mechanik 76 (1996) Suppl. 3, 295–298. [book]
[34] Gesztesy, F.; Holden, H.: On trace formulas for Schrödinger-type operators. Multiparticle quantum scattering with applications to nuclear, atomic and molecular physics (Minneapolis, MN, 1995), 121–145, IMA Vol. Math. Appl., 89, Springer, New York, 1997. [book]
[33] Gimse, T.; Holden, H.; Risebro, N. H.: Reservoir simulation by front tracking. Hyperbolic problems: theory, numerics, applications (Stony Brook, NY, 1994), 52–62, World Sci. Publ., River Edge, NJ, 1996. [book]
[32] Holden, H.; Lindstrøm, T.; Øksendal, B.; Ubøe, J.; Zhang, T.-S.: The stochastic Wick-type Burgers equation. Stochastic partial differential equations (Edinburgh, 1994), 141–161, London Math. Soc. Lecture Note Ser., 216, Cambridge Univ. Press, Cambridge, 1995. [book]
[31] Gesztesy, F.; Holden, H.: On new trace formulae for Schrödinger operators. KdV '95 (Amsterdam, 1995). Acta Appl. Math. 39 (1995), no. 1-3, 315–333. [article]
[30] Gjerde, Jon; Holden, Helge; Øksendal, Bernt; Ubøe, Jan; Zhang, Tu Sheng: An equation modelling transport of a substance in a stochastic medium. Seminar on Stochastic Analysis, Random Fields and Applications (Ascona, 1993), 123–134, Progr. Probab., 36, Birkhäuser, Basel, 1995. [book]
[29] Holden, Helge; Lindstrøm, Tom; Øksendal, Bernt; Ubøe, Jan; Zhang, Tu Sheng: A comparison experiment for Wick multiplication and ordinary multiplication. Stochastic analysis and related topics (Oslo, 1992), 149–159, Stochastics Monogr., 8, Gordon and Breach, Montreux, 1993. [book]
[28] Holden, Helge; Lindstrøm, Tom; Øksendal, Bernt; Ubøe, Jan: Discrete Wick products. Stochastic analysis and related topics (Oslo, 1992), 123–148, Stochastics Monogr., 8,Gordon and Breach, Montreux, 1993. [book]
[27] Gimse, Tore; Holden, Helge; Risebro, Nils Henrik: Recent results for conservation laws — theory, numerics and applications. Industrial Mathematics Week, Trondheim August 1992. Proceedings Department of Mathematical Sciences, NTH, 1993, pp. 131–144. [paper]
[26] Holden, Helge; Risebro, Nils Henrik: A mathematical model of traffic flow on a network of roads. Nonlinear hyperbolic problems: theoretical, applied, and computational aspects (Taormina, 1992), 329–335, Notes Numer. Fluid Mech., 43, Friedr. Vieweg, Braunschweig, 1993. [book]
[25] Bratvedt, F.; Bratvedt, K.; Buchholz, C.F.; Gimse, T.; Holden, H.; Holden, L.; Olufsen, R.; Risebro, N.H.: Three-dimensional reservoir simulation based on front tracking. North Sea Oil and Gas Reservoirs III, Kluwer, Dordrecht, 1993, pp. 247–257. [book]
[24] Albeverio, S.; Gielerak, R.; Holden, H.; Kolsrud, T.; Mebkhout, M.: Low temperature expansions around classical crystalline ground states. Stochastic Processes, Physics and Geometry II. World Scientific, Singapore, 1995, pp. 29–38. [book]
[23] Holden, H.; Holden, L.: A review of stochastic methods applied to reservoir evaluation. Stochastic Processes, Physics and Geometry II. World Scientific, Singapore, 1995, pp. 364–388. [book]
[22] Gjessing, H.; Holden, H.; Lindstrøm, T.; Øksendal, B.; Ubøe, J.; Zhang, T.-S.: The Wick product. Frontiers in Pure and Applied Probability, Volume I. VSP and TVP Science Publishers, Utrecht/Moscow, 1993, pp. 29–67. [book]
[21] Bratvedt, F.; Bratvedt, K.; Buchholz, C.F.; Gimse, T.; Holden, H.; Risebro, N.H.: Front tracking for groundwater simulations. Computational Methods in Water Resources IX. Vol. 1: Numerical Methods in Water Resources. Elsevier Applied Science, London–New York, 1992, pp. 97–104. [book]
[20] Bratvedt, F.; Bratvedt, K.; Buchholz, C.F.; Gimse, T.; Holden, H.; Holden, L.; Risebro, N.H.: Front tracking for petroleum reservoirs. Ideas and methods in mathematical analysis, stochastics, and applications (Oslo, 1988), 409–427, Cambridge Univ. Press, Cambridge, 1992. [paper]
[19] Holden, Helge; Holden, Lars: On scalar conservation laws in one dimension. Ideas and methods in mathematical analysis, stochastics, and applications (Oslo, 1988), 480–509, Cambridge Univ. Press, Cambridge, 1992. [paper]
[18] Gesztesy, F.; Holden, H.: A new representation of soliton solutions of the Kadomtsev-Petviashvili equation. Ideas and methods in mathematical analysis, stochastics, and applications (Oslo, 1988), 472–479, Cambridge Univ. Press, Cambridge, 1992. [paper]
[17] Holden, H.; Risebro, N. H.: A stochastic approach to conservation laws. Third International Conference on Hyperbolic Problems, Vol. I, II (Uppsala, 1990), 575–587, Studentlitteratur, Lund, 1991. [book]
[16] Holden, H.; Holden, L.; Risebro, N. H.: Some qualitative properties of 2×2 systems of conservation laws of mixed type. Nonlinear evolution equations that change type, 67–78, IMA Vol. Math. Appl., 27, Springer, New York, 1990. [article]
[15] Gesztesy, F.; Holden, H.; Šeba, P.: On point interactions in magnetic field systems. Schrödinger operators, standard and nonstandard (Dubna, 1988), 146–164, World Sci. Publ., Teaneck, NJ, 1989. [book]
[14] Albeverio, S.; Figari, R.; Gesztesy, F.; Høegh-Krohn, R.; Holden, H.; Kirsch, W.: Point interaction Hamiltonians for crystals with random defects. Applications of selfadjoint extensions in quantum physics (Dubna, 1987), 87–99, Lecture Notes in Phys., 324, Springer, Berlin, 1989. [book]
[13] Albeverio, S.; Høegh-Krohn, R.; Holden, H.; Kolsrud, T.: A covariant Feynman-Kac formula for unitary bundles over Euclidean space. Stochastic partial differential equations and applications, II (Trento, 1988), 1–12, Lecture Notes in Math., 1390, Springer, Berlin, 1989. [book]
[12 ] Holden, H.; Holden, L.: On some recent results for an explicit conservation law of mixed type in one dimension. Nonlinear hyperbolic equations—theory, computation methods, and applications (Aachen, 1988), 238–245, Notes Numer. Fluid Mech., 24, Friedr. Vieweg, Braunschweig,1989. [book]
[11] Albeverio, S.; Høegh-Krohn, R.; Holden, H.; Kolsrud, T.; Mebkhout, M.: A remark on the formation of crystals at zero temperature. Stochastic methods in mathematics and physics (Karpacz, 1988), 211–220, World Sci. Publ., Teaneck, NJ, 1989. [book]
[10] Holden, Helge; Holden, Lars: On the Riemann problem for a prototype of a mixed type conservation law. II. Current progress in hyperbolic systems: Riemann problems and computations (Brunswick, ME, 1988), 331–367, Contemp. Math., 100, Amer. Math. Soc., Providence, RI, 1989. [book]
[9] Holden, Helge: On some recent results for conservation laws in one dimension. Recent Developments in Mathematical Physics. Springer Proceedings in Physics, Springer-Verlag, Berlin, 1987, pp. 240–244. [book]
[8] Albeverio, S.; Gesztesy, F.; Høegh-Krohn, R.; Holden, H.; Kirsch, W.: The Schrödinger operator for a particle in a solid with deterministic and stochastic point interactions. Schrödinger operators, Aarhus 1985, 1–38, Lecture Notes in Math., 1218, Springer, Berlin, 1986. [article]
[7] Albeverio, Sergio; Høegh-Krohn, Raphael; Holden, Helge: Random fields with values in Lie groups and Higgs fields. Stochastic processes in classical and quantum systems (Ascona, 1985), 1–13, Lecture Notes in Phys., 262, Springer, Berlin, 1986. [article]
[6] Albeverio, Sergio; Høegh-Krohn, Raphael; Holden, Helge: Stochastic Lie group-valued measures and their relations to stochastic curve integrals, gauge fields and Markov cosurfaces. Stochastic processes—mathematics and physics (Bielefeld, 1984), 1–24, Lecture Notes in Math., 1158,Springer, Berlin, 1986. [article]
[5] Albeverio, S.; Høegh-Krohn, R.; Holden, H.: Markov processes on infinite dimensional spaces, Markov fields and Markov cosurfaces. Stochastic Space-Time Models and Limit Theorems. Reidel, Dordrecht-Boston-Lancaster 1984, pp. 11–40. [book]
[4] Albeverio, S.; Høegh-Krohn, R.; Holden, H.: Markov cosurfaces and gauge fields. Stochastic methods and computer techniques in quantum dynamics (Schladming, 1984), 211–231, Acta Phys. Austriaca Suppl., XXVI, Springer, Vienna, 1984. [book]
[3] Martinelli, Fabio; Holden, Helge: Lifshitz singularity of the integrated density of states and absence of diffusion near the bottom of the spectrum for a random Hamiltonian. Chaotic Behavior in Quantum Systems: Theory and Applications. Plenum Press, New York-London 1985, pp. 77–83. [book]
[2] Albeverio, S.; Høegh-Krohn, R.; Gesztesy, F.; Holden, H.: Some exactly solvable models in quantum mechanics and the low energy expansions. Proceedings of the second international conference on operator algebras, ideals, and their applications in theoretical physics (Leipzig, 1983), 12–28, Teubner-Texte Math., 67, Teubner, Leipzig, 1984. [book]
[1] Martinelli, Fabio; Holden, Helge: On absence of diffusion for low energy for a random Schrödinger operator on L2(Rν). Mathematical physics, VII (Boulder, Colo., 1983). Phys. A 124 (1984), no. 1-3, 413–417. [journal]
Miscellania
Holden, Helge, Risebro, Nils Henrik: Mathematical models of traffic flow. SIAM News, vol 54, no 5 (1 June 2021)