Edit Profile (opens in new tab) Holden, Helge Co-Author Distance Author ID: holden.helge Published as: Holden, Helge; Holden, H. Homepage: https://www.ntnu.edu/employees/holden External Links: MGP · ORCID · Wikidata · Google Scholar · dblp · GND · IdRef Documents Indexed: 194 Publications since 1983, including 11 Books 15 Contributions as Editor Biographic References: 1 Publication Co-Authors: 93 Co-Authors with 203 Joint Publications 2,956 Co-Co-Authors all top 5 Co-Authors 6 single-authored 54 Gesztesy, Fritz 36 Risebro, Nils Henrik 24 Karlsen, Kenneth Hvistendahl 19 Raynaud, Xavier 18 Høegh-Krohn, Raphael J. 17 Albeverio, Sergio A. 15 Piene, Ragni 13 Grunert, Katrin 13 Øksendal, Bernt Karsten 11 Teschl, Gerald 11 Ubøe, Jan 10 Lindstrøm, Tom L. 9 Coclite, Giuseppe Maria 9 Holden, Lars 9 Simon, Barry 9 Zhang, Tusheng S. 6 Lie, Knut-Andreas 5 Michor, Johanna 4 Hanche-Olsen, Harald 4 Nichols, Roger 4 Zhao, Zhongxin 3 Carrillo de la Plata, José Antonio 3 Colombo, Rinaldo M. 3 Kirsch, Werner 3 Koley, Ujjwal 3 Kolsrud, Torbjörn 3 Pang, Peter H. C. 3 Sande, Hilde 2 Behrndt, Jussi 2 Dutta, Rajib 2 Enolskiĭ, Viktor Zelikovich 2 Exner, Pavel 2 Fenstad, Jens Erik 2 Figari, Rodolfo 2 Gimse, Tore 2 Johannesen, Steinar 2 Jost, Jürgen 2 Karper, Trygve Klovning 2 Martinelli, Fabio 2 Mebkhout, Mohammed 2 Mitrovic, Darko 2 Paycha, Sylvie 2 Röckner, Michael 2 Scarlatti, Sergio 1 Babinsky, Holger 1 Boldrighini, Carlo 1 Bratvedt, Frode 1 Bratvedt, Kyrre 1 Bressan, Alberto 1 Buchholz, Christian F. 1 Bulla, W. 1 Bunimovich, Leonid Abramovich 1 Cascaval, Radu C. 1 Cellarosi, Francesco 1 Chen, Gui-Qiang G. 1 Clark, Steve 1 Cohen, Albert 1 De Lellis, Camillo 1 Deligne, Pierre René 1 Eckhardt, Jonathan 1 Ehrnström, Mats 1 Eilbeck, John Chris 1 Frank, Rupert L. 1 Frid, Hermano 1 Geronimo, Jeffrey S. 1 Gielerak, Roman 1 Gjerde, Jon 1 Gjessing, Håkon K. 1 Goldstein, Jerome Arthur 1 Grasmair, Markus 1 Gurarie, David 1 Gurevich, Boris 1 Holdahl, Runar 1 Holden, Steinar 1 Hu, Yaozhong 1 Illusie, Luc 1 Jensen, Arne 1 Khanin, Konstantin M. 1 Klaus, Martin 1 Kohn, Robert Vita 1 Kostenko, Aleksey S. 1 Latushkin, Yuri 1 Levitan, Boris Moiseevich 1 Li, Dong 1 Lubich, Christian 1 Malinnikova, Eugenia 1 Marcellini, Francesca 1 Martinsen, Torgeir With 1 Meyer, Yves F. 1 Munthe-Kaas, Hans Z. 1 Nasar, Sylvia 1 Nash, John Forbes jun. 1 Nirenberg, Louis 1 Onsager, Lars 1 Panov, Evgeniy Yu. 1 Pesin, Yakov Borisovich 1 Priuli, Fabio Simone 1 Ratkje, Signe Kjelstrup 1 Saab, Elias 1 Sadun, L. ...and 15 more Co-Authors all top 5 Serials 9 Discrete and Continuous Dynamical Systems 8 Journal of Differential Equations 6 Communications in Partial Differential Equations 6 SIAM Journal on Mathematical Analysis 5 Mathematics of Computation 4 Communications in Mathematical Physics 4 Journal of Mathematical Analysis and Applications 4 Journal of Functional Analysis 3 Reviews in Mathematical Physics 3 SIAM Journal on Applied Mathematics 3 Expositiones Mathematicae 3 Journal of Hyperbolic Differential Equations 3 Applied Mathematical Sciences 3 The Abel Prize 2 IMA Journal of Numerical Analysis 2 Journal of Computational Physics 2 Annales de l’Institut Fourier 2 BIT 2 Integral Equations and Operator Theory 2 Journal für die Reine und Angewandte Mathematik 2 Acta Applicandae Mathematicae 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 Revista Matemática Iberoamericana 2 IMRN. International Mathematics Research Notices 2 Journal of Physics A: Mathematical and General 2 Potential Analysis 2 Skrifter. Det Kongelige Norske Videnskabers Selskab 2 Cambridge Studies in Advanced Mathematics 2 CMS Conference Proceedings 2 Forum of Mathematics, Sigma 1 Archive for Rational Mechanics and Analysis 1 Computers & Mathematics with Applications 1 Communications on Pure and Applied Mathematics 1 Inverse Problems 1 Journal d’Analyse Mathématique 1 Journal of Mathematical Biology 1 Journal of Mathematical Physics 1 Journal of Statistical Physics 1 Letters in Mathematical Physics 1 Nonlinearity 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Applied Mathematics and Optimization 1 Journal of Optimization Theory and Applications 1 Mathematica Scandinavica 1 Memoirs of the American Mathematical Society 1 Normat 1 Numerische Mathematik 1 Quarterly of Applied Mathematics 1 SIAM Journal on Numerical Analysis 1 Studies in Applied Mathematics 1 Transactions of the American Mathematical Society 1 Journal of Operator Theory 1 Advances in Applied Mathematics 1 Probability Theory and Related Fields 1 Journal of Economic Dynamics & Control 1 Surveys on Mathematics for Industry 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Proceedings of the National Academy of Sciences of the United States of America 1 Stochastic Processes and their Applications 1 Bulletin of the American Mathematical Society. New Series 1 Annales de l’Institut Henri Poincaré. Physique Théorique 1 Electronic Journal of Differential Equations (EJDE) 1 European Mathematical Society Newsletter 1 Aerospace Science and Technology 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Computational Geosciences 1 Nonlinear Analysis. Real World Applications 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Stochastics 1 Contemporary Mathematics 1 Lecture Notes in Physics 1 Proceedings of Symposia in Pure Mathematics 1 Abel Symposia 1 Networks and Heterogeneous Media 1 International Journal of Differential Equations 1 Springer Proceedings in Mathematics & Statistics 1 Research in the Mathematical Sciences 1 World Scientific Series in 20th Century Physics 1 Universitext 1 Probability and its Applications 1 EMS Series of Lectures in Mathematics 1 EMS Series of Congress Reports 1 Texts and Monographs in Physics 1 London Mathematical Society. Newsletter 1 European Mathematical Society Magazine all top 5 Fields 132 Partial differential equations (35-XX) 34 Probability theory and stochastic processes (60-XX) 33 Numerical analysis (65-XX) 32 Fluid mechanics (76-XX) 27 Operator theory (47-XX) 26 Dynamical systems and ergodic theory (37-XX) 24 Quantum theory (81-XX) 23 History and biography (01-XX) 14 Ordinary differential equations (34-XX) 13 Statistical mechanics, structure of matter (82-XX) 12 Algebraic geometry (14-XX) 10 General and overarching topics; collections (00-XX) 9 Functional analysis (46-XX) 7 Global analysis, analysis on manifolds (58-XX) 7 Operations research, mathematical programming (90-XX) 4 Number theory (11-XX) 4 Group theory and generalizations (20-XX) 4 Difference and functional equations (39-XX) 4 Differential geometry (53-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Biology and other natural sciences (92-XX) 3 Mechanics of deformable solids (74-XX) 2 Combinatorics (05-XX) 2 Commutative algebra (13-XX) 2 Topological groups, Lie groups (22-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Special functions (33-XX) 2 Algebraic topology (55-XX) 2 Manifolds and cell complexes (57-XX) 2 Geophysics (86-XX) 1 Mathematical logic and foundations (03-XX) 1 Mechanics of particles and systems (70-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 171 Publications have been cited 3,430 times in 2,421 Documents Cited by ▼ Year ▼ Solvable models in quantum mechanics. Zbl 0679.46057Albeverio, Sergio; Gesztesy, Friedrich; Høegh-Krohn, Raphael; Holden, Helge 367 1988 Solvable models in quantum mechanics. With an appendix by Pavel Exner. 2nd revised ed. Zbl 1078.81003Albeverio, Sergio; Gesztesy, Friedrich; Høegh-Krohn, Raphael; Holden, Helge 161 2005 Global conservative solutions of the Camassa-Holm equation – a Lagrangian point of view. Zbl 1136.35080Holden, Helge; Raynaud, Xavier 151 2007 Soliton equations and their algebro-geometric solutions. I: (1+1)-dimensional continuous models. Zbl 1061.37056Gesztesy, Fritz; Holden, Helge 148 2003 Stochastic partial differential equations. A modeling, white noise functional approach. Zbl 0860.60045Holden, Helge; Øksendal, Bernt; Ubøe, Jan; Zhang, Tusheng 131 1996 The Kolmogorov-Riesz compactness theorem. Zbl 1208.46027Hanche-Olsen, Harald; Holden, Helge 106 2010 Front tracking for hyperbolic conservation laws. Zbl 1006.35002Holden, Helge; Risebro, Nils Henrik 105 2002 Dissipative solutions for the Camassa-Holm equation. Zbl 1178.65099Holden, Helge; Raynaud, Xavier 97 2009 Global weak solutions to a generalized hyperelastic-rod wave equation. Zbl 1100.35106Coclite, G. M.; Holden, H.; Karlsen, K. H. 93 2005 Front tracking for hyperbolic conservation laws. 2nd edition. Zbl 1346.35004Holden, Helge; Risebro, Nils Henrik 88 2015 A mathematical model of traffic flow on a network of unidirectional roads. Zbl 0833.35089Holden, Helge; Risebro, Nils Henrik 86 1995 Stochastic partial differential equations. A modeling, white noise functional approach. 2nd ed. Zbl 1198.60005Holden, Helge; Øksendal, Bernt; Ubøe, Jan; Zhang, Tusheng 72 2010 Wellposedness for a parabolic-elliptic system. Zbl 1082.35056Coclite, Giuseppe Maria; Holden, Helge; Karlsen, Kenneth Hvistendahl 69 2005 Splitting methods for partial differential equations with rough solutions. Analysis and Matlab programs. Zbl 1191.35005Holden, Helge; Karlsen, Kenneth H.; Lie, Knut-Andreas; Risebro, Nils Henrik 68 2010 Soliton equations and their algebro-geometric solutions. Volume II. \((1+1)\)-dimensional discrete models. Zbl 1151.37056Gesztesy, Fritz; Holden, Helge; Michor, Johanna; Teschl, Gerald 58 2008 Algebro-geometric solutions of the Camassa-Holm hierarchy. Zbl 1029.37049Gesztesy, Fritz; Holden, Helge 58 2003 A convergent numerical scheme for the Camassa-Holm equation based on multipeakons. Zbl 1111.35061Holden, Helge; Raynaud, Xavier 55 2006 Operator splitting for the KdV equation. Zbl 1219.35235Holden, Helge; Karlsen, Kenneth H.; Risebro, Nils Henrik; Tao, Terence 46 2011 Operator splitting for partial differential equations with Burgers nonlinearity. Zbl 1260.35184Holden, Helge; Lubich, Christian; Risebro, Nils Henrik 41 2013 Global conservative multipeakon solutions of the Camassa-Holm equation. Zbl 1128.65065Holden, Helge; Raynaud, Xavier 38 2007 Well-posedness of higher-order Camassa-Holm equations. Zbl 1186.35003Coclite, G. M.; Holden, H.; Karlsen, K. H. 37 2009 Global solutions for the two-component Camassa-Holm system. Zbl 1258.35176Grunert, Katrin; Holden, Helge; Raynaud, Xavier 36 2012 Periodic conservative solutions of the Camassa-Holm equation. Zbl 1158.35079Holden, Helge; Raynaud, Xavier 35 2008 Algebro-geometric quasi-periodic finite-gap solutions of the Toda and Kac-van Moerbeke hierarchies. Zbl 0906.35099Bulla, W.; Gesztesy, F.; Holden, H.; Teschl, G. 34 1998 Convergence of a finite difference scheme for the Camassa-Holm equation. Zbl 1122.76065Holden, Helge; Raynaud, Xavier 33 2006 Algebro-geometric solutions of the Baxter-Szegő difference equation. Zbl 1080.37075Geronimo, Jeffrey S.; Gesztesy, Fritz; Holden, Helge 32 2005 Operator splitting methods for generalized Korteweg-de Vries equations. Zbl 0947.65102Holden, Helge; Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik 32 1999 Global conservative solutions of the generalized hyperelastic-rod wave equation. Zbl 1116.35115Holden, Helge; Raynaud, Xavier 32 2007 Lipschitz metric for the Hunter-Saxton equation. Zbl 1195.35046Bressan, Alberto; Holden, Helge; Raynaud, Xavier 31 2010 On absence of diffusion near the bottom of the spectrum for a random Schrödinger operator on \(L^ 2({\mathbb{R}}^ v)^+\). Zbl 0546.60063Martinelli, Fabio; Holden, Helge 30 1984 Conservation laws with a random source. Zbl 0885.35069Holden, H.; Risebro, N. H. 29 1997 Borg-type theorems for matrix-valued Schrödinger operators. Zbl 0970.34073Clark, Steve; Gesztesy, Fritz; Holden, Helge; Levitan, Boris M. 29 2000 The Burgers equation with a noisy force and the stochastic heat equation. Zbl 0804.35158Holden, Helge; Lindstrøm, Tom; Øksendal, Bernt; Ubøe, J.; Zhang, T.-S. 28 1994 Global semigroup of conservative solutions of the nonlinear variational wave equation. Zbl 1270.35322Holden, Helge; Raynaud, Xavier 28 2011 A numerical method for first order nonlinear scalar conservation laws in one-dimension. Zbl 0658.65085Holden, Helge; Holden, Lars; Høegh-Krohn, Raphael 27 1988 Global dissipative multipeakon solutions of the Camassa-Holm equation. Zbl 1156.76014Holden, H.; Raynaud, X. 24 2008 Front tracking for hyperbolic conservation laws. Paperback ed. Zbl 1239.35003Holden, Helge; Risebro, Nils Henrik 23 2011 Real-valued algebro-geometric solutions of the Camassa-Holm hierarchy. Zbl 1153.37427Gesztesy, Fritz; Holden, Helge 22 2008 Lipschitz metric for the Camassa-Holm equation on the line. Zbl 1297.35205Grunert, Katrin; Holden, Helge; Raynaud, Xavier 21 2013 A new class of solvable models in quantum mechanics describing point interactions on the line. Zbl 0627.34030Gesztesy, F.; Holden, H. 20 1987 Trapping and cascading of eigenvalues in the large coupling limit. Zbl 0669.35085Gesztesy, F.; Gurarie, D.; Holden, H.; Klaus, M.; Sadun, L.; Simon, B.; Vogl, P. 20 1988 The continuum limit of follow-the-leader models – a short proof. Zbl 1378.35180Holden, Helge; Risebro, Nils Henrik 20 2018 Lipschitz metric for the periodic Camassa-Holm equation. Zbl 1205.35252Grunert, Katrin; Holden, Helge; Raynaud, Xavier 19 2011 Symmetric waves are traveling waves. Zbl 1181.35230Ehrnström, Mats; Holden, Helge; Raynaud, Xavier 18 2009 On the Riemann problem for a prototype of a mixed type conservation law. Zbl 0637.35051Holden, Helge 17 1987 The damped string problem revisited. Zbl 1223.47049Gesztesy, Fritz; Holden, Helge 16 2011 A continuous interpolation between conservative and dissipative solutions for the two-component Camassa-Holm system. Zbl 1315.35186Grunert, Katrin; Holden, Helge; Raynaud, Xavier 16 2015 Convergent difference schemes for the Hunter–Saxton equation. Zbl 1114.65101Holden, H.; Karlsen, K. H.; Risebro, N. H. 16 2007 A unified approach to eigenvalues and resonances of Schrödinger operators using Fredholm determinants. Zbl 0622.35049Gesztesy, F.; Holden, H. 15 1987 Unconditionally stable splitting methods for the shallow water equations. Zbl 0945.76059Holdahl, Runar; Holden, Helge; Lie, Knut-Andreas 15 1999 Higher order trace relations for Schrödinger operators. Zbl 0833.34084Gesztesy, Fritz; Holden, Helge; Simon, Barry; Zhao, Zhong Xin 15 1995 Global conservative solutions to the Camassa-Holm equation for initial data with nonvanishing asymptotics. Zbl 1253.35147Grunert, Katrin; Holden, Helge; Raynaud, Xavier 14 2012 The solution of the Cauchy problem with large data for a model of a mixture of gases. Zbl 1178.35248Holden, Helge; Risebro, Nils Henrik; Sande, Hilde 14 2009 Global dissipative solutions of the two-component Camassa-Holm system for initial data with nonvanishing asymptotics. Zbl 1295.35193Grunert, Katrin; Holden, Helge; Raynaud, Xavier 14 2014 A trace formula for multidimensional Schrödinger operators. Zbl 0864.35030Gesztesy, F.; Holden, H.; Simon, B.; Zhao, Z. 14 1996 Follow-the-leader models can be viewed as a numerical approximation to the Lighthill-Whitham-Richards model for traffic flow. Zbl 1414.35122Holden, Helge; Risebro, Nils Henrik 14 2018 Models for dense multilane vehicular traffic. Zbl 1441.35162Holden, Helge; Risebro, Nils Henrik 14 2019 On the Toda and Kac-van Moerbeke systems. Zbl 0789.58043Gesztesy, Fritz; Holden, Helge; Simon, Barry; Zhao, Zhong Xin 13 1993 Trace formulae and inverse spectral theory for Schrödinger operators. Zbl 0786.34081Gesztesy, Fritz; Holden, Helge; Simon, Barry; Zhao, Zhong Xin 13 1993 Absolute summability of the trace relation for certain Schrödinger operators. Zbl 0821.34076Gesztesy, Fritz; Holden, Helge; Simon, Barry 13 1995 On trace formulas for Schrödinger-type operators. Zbl 0881.34027Gesztesy, F.; Holden, H. 13 1997 An improvement of the Kolmogorov-Riesz compactness theorem. Zbl 1425.46018Hanche-Olsen, Harald; Holden, Helge; Malinnikova, Eugenia 13 2019 Operator splitting methods for degenerate convection-diffusion equations. II: Numerical examples with emphasis on reservoir simulation and sedimentation. Zbl 1049.35113Holden, Helge; Karlsen, Kenneth Hvistendahl; Lie, Knut-Andreas 12 2000 An unconditionally stable method for the Euler equations. Zbl 0922.76251Holden, Helge; Lie, Knut-Andreas; Risebro, Nils Henrik 12 1999 Riemann problems with a kink. Zbl 0926.35087Holden, Helge; Risebro, Nils Henrik 12 1999 Convergence of a fully discrete finite difference scheme for the Korteweg-de Vries equation. Zbl 1348.65121Holden, Helge; Koley, Ujjwal; Risebro, Nils Henrik 12 2015 A method of fractional steps for scalar conservation laws without the CFL conditions. Zbl 0799.35150Holden, Helge; Risebro, Nils Henrik 11 1993 On energy gaps in a new type of analytically solvable model in quantum mechanics. Zbl 0669.47002Gesztesy, F.; Holden, H.; Kirsch, W. 11 1988 Stochastic multiplicative measures, generalized Markov semigroups, and group-valued stochastic processes and fields. Zbl 0639.60010Albeverio, Sergio; Høegh-Krohn, Raphael; Holden, Helge 10 1988 On uniqueness and existence of entropy solutions of weakly coupled systems of nonlinear degenerate parabolic equations. Zbl 1036.35102Holden, Helge; Karlsen, Kenneth H.; Risebro, Nils H. 10 2003 Abstract wave equations and associated Dirac-type operators. Zbl 1262.35174Gesztesy, Fritz; Goldstein, Jerome A.; Holden, Helge; Teschl, Gerald 10 2012 A stochastic approach to conservation laws. Zbl 0789.35103Holden, H.; Risebro, N. H. 10 1991 Representation and construction of multiplicative noise. Zbl 0696.60012Albeverio, Sergio; Holden, Helge; Høegh-Krohn, Raphael; Kolsrud, Torbjörn 10 1989 Explicit construction of solutions of the modified Kadomtsev-Petviashvili equation. Zbl 0728.35104Gesztesy, F.; Holden, H.; Saab, E.; Simon, B. 9 1991 The general peakon-antipeakon solution for the Camassa-Holm equation. Zbl 1352.35146Grunert, Katrin; Holden, Helge 9 2016 FRONTLINE and FRONTSIM: Two full scale, two-phase, black oil reservoir simulators based on front tracking. Zbl 0780.76073Bratvedt, Frode; Bratvedt, Kyrre; Buchholz, Christian F.; Gimse, Tore; Holden, Helge; Holden, Lars; Risebro, Nils Henrik 8 1993 Trace formulas and conservation laws for nonlinear evolution equations. Zbl 0805.35113Gesztesy, F.; Holden, H. 8 1994 Stability of solutions of quasilinear parabolic equations. Zbl 1078.35047Coclite, Giuseppe Maria; Holden, Helge 8 2005 Operator splitting methods for degenerate convection-diffusion equations. I: Convergence and entropy estimates. Zbl 0974.35065Holden, Helge; Karlsen, Kenneth Hvistendahl; Lie, Knut-Andreas 8 2000 The pressure equation for fluid flow in a stochastic medium. Zbl 0834.60068Holden, H.; Lindstrøm, T.; Øksendal, B.; Ubøe, J.; Zhang, T.-S. 8 1995 A numerical scheme based on multipeakons for conservative solutions of the Camassa-Holm equation. Zbl 1138.65093Holden, H.; Raynaud, X. 8 2008 A convergent finite-difference method for a nonlinear variational wave equation. Zbl 1236.65112Holden, H.; Karlsen, K. H.; Risebro, N. H. 8 2009 Stochastic boundary value problems: A white noise functional approach. Zbl 0792.60055Holden, Helge; Lindstrøm, Tom; Øksendal, Bernt; Ubøe, Jan; Zhang, Tu-Sheng 7 1993 The Wick product. Zbl 0820.60048Gjessing, H.; Holden, Helge; Lindstrøm, Tom; Øksendal, Bernt; Ubøe, J.; Zhang, T.-S. 7 1993 Local conservation laws and the Hamiltonian formalism for the Ablowitz-Ladik hierarchy. Zbl 1193.37092Gesztesy, Fritz; Holden, Helge; Michor, Johanna; Teschl, Gerald 7 2008 Point interactions in two dimensions: basic properties, approximations and applications in solid state physics. Zbl 0619.35030Albeverio, Sergio; Gesztesy, Friedrich; Høegh-Krohn, Raphael; Holden, Helge 7 1987 Darboux-type transformations and hyperelliptic curves. Zbl 1102.14301Gesztesy, Fritz; Holden, Helge 7 2000 Periodic conservative solutions for the two-component Camassa-Holm system. Zbl 1320.35311Grunert, Katrin; Holden, Helge; Raynaud, Xavier 7 2013 Front tracking for a model of immiscible gas flow with large data. Zbl 1425.76214Holden, Helge; Risebro, Nils Henrik; Sande, Hilde 7 2010 Dirichlet-to-Neumann maps, abstract Weyl-Titchmarsh \(M\)-functions, and a generalized index of unbounded meromorphic operator-valued functions. Zbl 1350.47009Behrndt, Jussi; Gesztesy, Fritz; Holden, Helge; Nichols, Roger 7 2016 A Lipschitz metric for the Hunter-Saxton equation. Zbl 1420.35305Carrillo, José Antonio; Grunert, Katrin; Holden, Helge 7 2019 Strong compactness of approximate solutions to degenerate elliptic-hyperbolic equations with discontinuous flux function. Zbl 1212.35166Holden, Helge; Karlsen, Kenneth H.; Mitrovic, Darko; Panov, Evgueni Yu. 6 2009 On scalar conservation laws in one dimension. Zbl 0851.65064Holden, Helge; Holden, Lars 6 1992 On coupling constant thresholds in two dimensions. Zbl 0593.35031Holden, Helge 6 1985 On new trace formulae for Schrödinger operators. Zbl 0830.35118Gesztesy, F.; Holden, H. 6 1995 Markov cosurfaces and gauge fields. Zbl 0541.60093Albeverio, Sergio; Høegh-Krohn, Raphael; Holden, Helge 6 1984 The short range expansion. Zbl 0546.35019Holden, Helge; Høegh-Krohn, Raphael; Johannesen, Steinar 6 1983 Convergence of finite difference schemes for the Benjamin-Ono equation. Zbl 1353.65090Dutta, Rajib; Holden, Helge; Koley, Ujjwal; Risebro, Nils Henrik 6 2016 The Hunter-Saxton equation with noise. Zbl 1451.35266Holden, Helge; Karlsen, Kenneth H.; Pang, Peter H. C. 6 2021 Discrete Wick calculus and stochastic functional equations. Zbl 0776.60067Holden, Helge; Lindstrøm, Tom; Øksendal, Bernt; Ubøe, Jan 5 1992 Global well-posedness of the viscous Camassa-Holm equation with gradient noise. Zbl 1515.35376Holden, Helge; Karlsen, Kenneth H.; Pang, Peter H. C. 2 2023 Noise-driven bifurcations in a neural field system modelling networks of grid cells. Zbl 1500.92004Carrillo, José A.; Holden, Helge; Solem, Susanne 1 2022 Uniqueness of conservative solutions for the Hunter-Saxton equation. Zbl 1486.35005Grunert, Katrin; Holden, Helge 1 2022 The Hunter-Saxton equation with noise. Zbl 1451.35266Holden, Helge; Karlsen, Kenneth H.; Pang, Peter H. C. 6 2021 Evolutionarily stable strategies in stable and periodically fluctuating populations: the Rosenzweig-MacArthur predator-prey model. Zbl 1485.92087Grunert, Katrin; Holden, Helge; Stenseth, Nils Chr. 2 2021 Singular diffusion with Neumann boundary conditions. Zbl 1459.35230Coclite, Giuseppe Maria; Holden, Helge; Risebro, Nils Henrik 1 2021 A Lipschitz metric for the Camassa-Holm equation. Zbl 1442.35371Carrillo, José A.; Grunert, Katrin; Holden, Helge 1 2020 On the microscopic modeling of vehicular traffic on general networks. Zbl 1448.90034Colombo, Rinaldo M.; Holden, Helge; Marcellini, Francesca 1 2020 Models for dense multilane vehicular traffic. Zbl 1441.35162Holden, Helge; Risebro, Nils Henrik 14 2019 An improvement of the Kolmogorov-Riesz compactness theorem. Zbl 1425.46018Hanche-Olsen, Harald; Holden, Helge; Malinnikova, Eugenia 13 2019 A Lipschitz metric for the Hunter-Saxton equation. Zbl 1420.35305Carrillo, José Antonio; Grunert, Katrin; Holden, Helge 7 2019 The Abel Prize 2013–2017. Zbl 1419.01001 1 2019 The continuum limit of follow-the-leader models – a short proof. Zbl 1378.35180Holden, Helge; Risebro, Nils Henrik 20 2018 Follow-the-leader models can be viewed as a numerical approximation to the Lighthill-Whitham-Richards model for traffic flow. Zbl 1414.35122Holden, Helge; Risebro, Nils Henrik 14 2018 On the equivalence of Eulerian and Lagrangian variables for the two-component Camassa-Holm system. Zbl 1406.35277Grasmair, Markus; Grunert, Katrin; Holden, Helge 2 2018 Real-valued algebro-geometric solutions of the two-component Camassa-Holm hierarchy. (Solutions algebro-géométriques à valeurs réelles de la hierarchie de Camassa-Holm à deux composantes.) Zbl 1383.35182Eckhardt, Jonathan; Gesztesy, Fritz; Holden, Helge; Kostenko, Aleksey; Teschl, Gerald 5 2017 On the index of meromorphic operator-valued functions and some applications. Zbl 1441.47012Behrndt, Jussi; Gesztesy, Fritz; Holden, Helge; Nichols, Roger 1 2017 The general peakon-antipeakon solution for the Camassa-Holm equation. Zbl 1352.35146Grunert, Katrin; Holden, Helge 9 2016 Dirichlet-to-Neumann maps, abstract Weyl-Titchmarsh \(M\)-functions, and a generalized index of unbounded meromorphic operator-valued functions. Zbl 1350.47009Behrndt, Jussi; Gesztesy, Fritz; Holden, Helge; Nichols, Roger 7 2016 Convergence of finite difference schemes for the Benjamin-Ono equation. Zbl 1353.65090Dutta, Rajib; Holden, Helge; Koley, Ujjwal; Risebro, Nils Henrik 6 2016 On the Braess paradox with nonlinear dynamics and control theory. Zbl 1335.35154Colombo, Rinaldo M.; Holden, Helge 4 2016 Isentropic fluid dynamics in a curved pipe. Zbl 1362.35182Colombo, Rinaldo M.; Holden, Helge 3 2016 Addendum to “The Kolmogorov-Riesz compactness theorem” [Expo. Math. 28 (2010) 385-394]. Zbl 1356.46022Hanche-Olsen, Harald; Holden, Helge 3 2016 Erratum to: “On factorizations of analytic operator-valued functions and eigenvalue multiplicity questions”. Zbl 1465.47010Gesztesy, Fritz; Holden, Helge; Nichols, Roger 3 2016 Front tracking for hyperbolic conservation laws. 2nd edition. Zbl 1346.35004Holden, Helge; Risebro, Nils Henrik 88 2015 A continuous interpolation between conservative and dissipative solutions for the two-component Camassa-Holm system. Zbl 1315.35186Grunert, Katrin; Holden, Helge; Raynaud, Xavier 16 2015 Convergence of a fully discrete finite difference scheme for the Korteweg-de Vries equation. Zbl 1348.65121Holden, Helge; Koley, Ujjwal; Risebro, Nils Henrik 12 2015 Operator splitting for the Benjamin-Ono equation. Zbl 1326.35311Dutta, R.; Holden, H.; Koley, U.; Risebro, N. H. 4 2015 On factorizations of analytic operator-valued functions and eigenvalue multiplicity questions. Zbl 1316.47014Gesztesy, Fritz; Holden, Helge; Nichols, Roger 2 2015 Global dissipative solutions of the two-component Camassa-Holm system for initial data with nonvanishing asymptotics. Zbl 1295.35193Grunert, Katrin; Holden, Helge; Raynaud, Xavier 14 2014 On an inverse problem for scalar conservation laws. Zbl 1286.35266Holden, Helge; Priuli, Fabio Simone; Risebro, Nils Henrik 3 2014 List of publications for Endre Szemerédi. Zbl 1317.01031Holden, Helge; Piene, Ragni 1 2014 Operator splitting for partial differential equations with Burgers nonlinearity. Zbl 1260.35184Holden, Helge; Lubich, Christian; Risebro, Nils Henrik 41 2013 Lipschitz metric for the Camassa-Holm equation on the line. Zbl 1297.35205Grunert, Katrin; Holden, Helge; Raynaud, Xavier 21 2013 Periodic conservative solutions for the two-component Camassa-Holm system. Zbl 1320.35311Grunert, Katrin; Holden, Helge; Raynaud, Xavier 7 2013 Operator splitting for two-dimensional incompressible fluid equations. Zbl 1322.76017Holden, Helge; Karlsen, Kenneth H.; Karper, Trygve 2 2013 Operator splitting for well-posed active scalar equations. Zbl 1282.35305Holden, Helge; Karlsen, Kenneth H.; Karper, Trygve K. 1 2013 Optimal rebalancing of portfolios with transaction costs. Zbl 1285.91118Holden, Helge; Holden, Lars 1 2013 Global solutions for the two-component Camassa-Holm system. Zbl 1258.35176Grunert, Katrin; Holden, Helge; Raynaud, Xavier 36 2012 Global conservative solutions to the Camassa-Holm equation for initial data with nonvanishing asymptotics. Zbl 1253.35147Grunert, Katrin; Holden, Helge; Raynaud, Xavier 14 2012 Abstract wave equations and associated Dirac-type operators. Zbl 1262.35174Gesztesy, Fritz; Goldstein, Jerome A.; Holden, Helge; Teschl, Gerald 10 2012 Nonlinear partial differential equations. The Abel symposium 2010. Proceedings of the Abel symposium, Oslo, Norway, September 28–October 2, 2010. Zbl 1231.35003 1 2012 Operator splitting for the KdV equation. Zbl 1219.35235Holden, Helge; Karlsen, Kenneth H.; Risebro, Nils Henrik; Tao, Terence 46 2011 Global semigroup of conservative solutions of the nonlinear variational wave equation. Zbl 1270.35322Holden, Helge; Raynaud, Xavier 28 2011 Front tracking for hyperbolic conservation laws. Paperback ed. Zbl 1239.35003Holden, Helge; Risebro, Nils Henrik 23 2011 Lipschitz metric for the periodic Camassa-Holm equation. Zbl 1205.35252Grunert, Katrin; Holden, Helge; Raynaud, Xavier 19 2011 The damped string problem revisited. Zbl 1223.47049Gesztesy, Fritz; Holden, Helge 16 2011 \(L^\infty\) solutions for a model of nonisothermal polytropic gas flow. Zbl 1252.35197Frid, Hermano; Holden, Helge; Karlsen, Kenneth H. 2 2011 The Kolmogorov-Riesz compactness theorem. Zbl 1208.46027Hanche-Olsen, Harald; Holden, Helge 106 2010 Stochastic partial differential equations. A modeling, white noise functional approach. 2nd ed. Zbl 1198.60005Holden, Helge; Øksendal, Bernt; Ubøe, Jan; Zhang, Tusheng 72 2010 Splitting methods for partial differential equations with rough solutions. Analysis and Matlab programs. Zbl 1191.35005Holden, Helge; Karlsen, Kenneth H.; Lie, Knut-Andreas; Risebro, Nils Henrik 68 2010 Lipschitz metric for the Hunter-Saxton equation. Zbl 1195.35046Bressan, Alberto; Holden, Helge; Raynaud, Xavier 31 2010 Front tracking for a model of immiscible gas flow with large data. Zbl 1425.76214Holden, Helge; Risebro, Nils Henrik; Sande, Hilde 7 2010 The algebro-geometric initial value problem for the Ablowitz-Ladik hierarchy. Zbl 1178.37074Gesztesy, Fritz; Holden, Helge; Michor, Johanna; Teschl, Gerald 3 2010 Contract adjustment under uncertainty. Zbl 1202.91031Holden, Helge; Holden, Lars; Holden, Steinar 1 2010 Ground states of the Schrödinger-Maxwell system with Dirac mass: existence and asymptotics. Zbl 1190.35189Coclite, Giuseppe Maria; Holden, Helge 1 2010 Dissipative solutions for the Camassa-Holm equation. Zbl 1178.65099Holden, Helge; Raynaud, Xavier 97 2009 Well-posedness of higher-order Camassa-Holm equations. Zbl 1186.35003Coclite, G. M.; Holden, H.; Karlsen, K. H. 37 2009 Symmetric waves are traveling waves. Zbl 1181.35230Ehrnström, Mats; Holden, Helge; Raynaud, Xavier 18 2009 The solution of the Cauchy problem with large data for a model of a mixture of gases. Zbl 1178.35248Holden, Helge; Risebro, Nils Henrik; Sande, Hilde 14 2009 A convergent finite-difference method for a nonlinear variational wave equation. Zbl 1236.65112Holden, H.; Karlsen, K. H.; Risebro, N. H. 8 2009 Strong compactness of approximate solutions to degenerate elliptic-hyperbolic equations with discontinuous flux function. Zbl 1212.35166Holden, Helge; Karlsen, Kenneth H.; Mitrovic, Darko; Panov, Evgueni Yu. 6 2009 The Ablowitz-Ladik hierarchy revisited. Zbl 1160.37028Gesztesy, Fritz; Holden, Helge; Michor, Johanna; Teschl, Gerald 4 2009 Zero diffusion-dispersion-smoothing limits for a scalar conservation law with discontinuous flux function. Zbl 1206.35170Holden, H.; Karlsen, K. H.; Mitrovic, D. 3 2009 Convergence of front tracking and the Glimm scheme for a model of the flow of immiscible gases. Zbl 1404.65119Holden, Helge; Risebro, Nils Henrik; Sande, Hilde 1 2009 Soliton equations and their algebro-geometric solutions. Volume II. \((1+1)\)-dimensional discrete models. Zbl 1151.37056Gesztesy, Fritz; Holden, Helge; Michor, Johanna; Teschl, Gerald 58 2008 Periodic conservative solutions of the Camassa-Holm equation. Zbl 1158.35079Holden, Helge; Raynaud, Xavier 35 2008 Global dissipative multipeakon solutions of the Camassa-Holm equation. Zbl 1156.76014Holden, H.; Raynaud, X. 24 2008 Real-valued algebro-geometric solutions of the Camassa-Holm hierarchy. Zbl 1153.37427Gesztesy, Fritz; Holden, Helge 22 2008 A numerical scheme based on multipeakons for conservative solutions of the Camassa-Holm equation. Zbl 1138.65093Holden, H.; Raynaud, X. 8 2008 Local conservation laws and the Hamiltonian formalism for the Ablowitz-Ladik hierarchy. Zbl 1193.37092Gesztesy, Fritz; Holden, Helge; Michor, Johanna; Teschl, Gerald 7 2008 The algebro-geometric Toda hierarchy initial value problem for complex-valued initial data. Zbl 1143.37045Gesztesy, Fritz; Holden, Helge; Teschl, Gerald 5 2008 Global weak solutions for a shallow water equation. Zbl 1168.35415Coclite, G. M.; Holden, H.; Karlsen, K. H. 1 2008 Erratum to: “The Schrödinger-Maxwell system with Dirac mass” [Ann. Inst. H. Poincaré Anal. Non Linéaire 24 (5) (2007) 773-793]. Zbl 1157.35334Coclite, G. M.; Holden, H. 1 2008 A combined experimental and numerical study of flow structures over three-dimensional shock control bumps. Zbl 1273.76262Wong, W. S.; Qin, N.; Sellars, N.; Holden, H.; Babinsky, H. 1 2008 Global conservative solutions of the Camassa-Holm equation – a Lagrangian point of view. Zbl 1136.35080Holden, Helge; Raynaud, Xavier 151 2007 Global conservative multipeakon solutions of the Camassa-Holm equation. Zbl 1128.65065Holden, Helge; Raynaud, Xavier 38 2007 Global conservative solutions of the generalized hyperelastic-rod wave equation. Zbl 1116.35115Holden, Helge; Raynaud, Xavier 32 2007 Convergent difference schemes for the Hunter–Saxton equation. Zbl 1114.65101Holden, H.; Karlsen, K. H.; Risebro, N. H. 16 2007 The Schrödinger-Maxwell system with Dirac mass. Zbl 1132.35024Coclite, G. M.; Holden, H. 5 2007 Algebro-geometric finite-band solutions of the Ablowitz-Ladik hierarchy. Zbl 1137.37033Gesztesy, Fritz; Holden, Helge; Michor, Johanna; Teschl, Gerald 3 2007 A convergent numerical scheme for the Camassa-Holm equation based on multipeakons. Zbl 1111.35061Holden, Helge; Raynaud, Xavier 55 2006 Convergence of a finite difference scheme for the Camassa-Holm equation. Zbl 1122.76065Holden, Helge; Raynaud, Xavier 33 2006 Local conservation laws and the Hamiltonian formalism for the Toda hierarchy revisited. Zbl 1162.37326Gesztesy, Fritz; Holden, Helge 1 2006 Solvable models in quantum mechanics. With an appendix by Pavel Exner. 2nd revised ed. Zbl 1078.81003Albeverio, Sergio; Gesztesy, Friedrich; Høegh-Krohn, Raphael; Holden, Helge 161 2005 Global weak solutions to a generalized hyperelastic-rod wave equation. Zbl 1100.35106Coclite, G. M.; Holden, H.; Karlsen, K. H. 93 2005 Wellposedness for a parabolic-elliptic system. Zbl 1082.35056Coclite, Giuseppe Maria; Holden, Helge; Karlsen, Kenneth Hvistendahl 69 2005 Algebro-geometric solutions of the Baxter-Szegő difference equation. Zbl 1080.37075Geronimo, Jeffrey S.; Gesztesy, Fritz; Holden, Helge 32 2005 Stability of solutions of quasilinear parabolic equations. Zbl 1078.35047Coclite, Giuseppe Maria; Holden, Helge 8 2005 Spectral analysis of Darboux transformations for the focusing NLS hierarchy. Zbl 1097.34063Cascaval, Radu C.; Gesztesy, Fritz; Holden, Helge; Latushkin, Yuri 5 2004 Soliton equations and their algebro-geometric solutions. I: (1+1)-dimensional continuous models. Zbl 1061.37056Gesztesy, Fritz; Holden, Helge 148 2003 Algebro-geometric solutions of the Camassa-Holm hierarchy. Zbl 1029.37049Gesztesy, Fritz; Holden, Helge 58 2003 On uniqueness and existence of entropy solutions of weakly coupled systems of nonlinear degenerate parabolic equations. Zbl 1036.35102Holden, Helge; Karlsen, Kenneth H.; Risebro, Nils H. 10 2003 The hyperelliptic \(\zeta\)-function and the integrable massive Thirring model. Zbl 1101.14314Eilbeck, J. C.; Enolskii, V. Z.; Holden, H. 4 2003 Front tracking for hyperbolic conservation laws. Zbl 1006.35002Holden, Helge; Risebro, Nils Henrik 105 2002 Dubrovin equations and integrable systems on hyperelliptic curves. Zbl 1075.35068Gesztesy, Fritz; Holden, Helge 1 2002 Operator splitting for convection-dominated nonlinear partial differential equations. Zbl 0989.65093Holden, Helge; Karlsen, Kenneth Hvistendahl; Lie, Knut-Andreas; Risebro, Nils Henrik 1 2001 Borg-type theorems for matrix-valued Schrödinger operators. Zbl 0970.34073Clark, Steve; Gesztesy, Fritz; Holden, Helge; Levitan, Boris M. 29 2000 Operator splitting methods for degenerate convection-diffusion equations. II: Numerical examples with emphasis on reservoir simulation and sedimentation. Zbl 1049.35113Holden, Helge; Karlsen, Kenneth Hvistendahl; Lie, Knut-Andreas 12 2000 Operator splitting methods for degenerate convection-diffusion equations. I: Convergence and entropy estimates. Zbl 0974.35065Holden, Helge; Karlsen, Kenneth Hvistendahl; Lie, Knut-Andreas 8 2000 ...and 71 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,708 Authors 65 Holden, Helge 52 Coclite, Giuseppe Maria 51 Gesztesy, Fritz 50 Risebro, Nils Henrik 46 Albeverio, Sergio A. 43 Karlsen, Kenneth Hvistendahl 41 Geng, Xianguo 31 Exner, Pavel 23 Mi, Yongsheng 23 Yin, Zhaoyang 22 Malamud, Mark M. 22 Teschl, Gerald 21 Mu, Chunlai 20 Chen, Geng 20 Liu, Yue 18 Behrndt, Jussi 18 Bürger, Raimund 18 Fan, Engui 18 Grunert, Katrin 18 Øksendal, Bernt Karsten 18 Posilicano, Andrea 17 Bressan, Alberto 17 Di Ruvo, Lorenzo 17 Geyler, Vladimir A. 17 Piccoli, Benedetto 17 Simon, Barry 16 Kostenko, Aleksey S. 16 Lai, Shaoyong 16 Ma, Wen-Xiu 16 Raynaud, Xavier 15 Herty, Michael Matthias 15 Popov, Igor’ Yur’evich 15 Qiao, Zhijun 15 Teta, Alessandro 14 Garavello, Mauro 14 Michelangeli, Alessandro 13 Colombo, Rinaldo M. 13 Eckhardt, Jonathan 13 Goatin, Paola 13 Koshmanenko, Volodymyr Dmytrovych 13 Qu, Changzheng 12 Göttlich, Simone 12 Guo, Boling 12 Mishra, Siddhartha 12 Xie, Yingchao 12 Xue, Bo 12 Yang, Chuanfu 12 Zeng, Xin 11 Høegh-Krohn, Raphael J. 11 Kurasov, Pavel B. 11 Šeba, Petr 11 Towers, John D. 11 Wei, Jiao 10 Alpay, Daniel Aron 10 Borisov, Denis Ivanovich 10 Hu, Yanbo 10 Ostermann, Alexander 10 Zhao, Peng 9 Cacciapuoti, Claudio 9 Cai, Hong 9 Carlone, Raffaele 9 He, Guoliang 9 Hu, Qiaoyi 9 Lanconelli, Alberto 9 Levajković, Tijana 9 Schratz, Katharina 9 Seleši, Dora 8 Corli, Andrea 8 Figari, Rodolfo 8 Fjordholm, Ulrik Skre 8 Hou, Yu 8 Koley, Ujjwal 8 Korotyaev, Evgeny L. 8 Liu, Zhengrong 8 Lotoreichik, Vladimir 8 Noja, Diego 8 Schwab, Christoph 8 Tang, Hao 8 Tian, Lixin 8 Ubøe, Jan 8 Wang, Yujuan 8 Wu, Lihua 8 Zhang, Hongqing 7 Chen, Gui-Qiang G. 7 Chen, Jinbing 7 Dell’Antonio, Gian Fausto 7 Ding, Danping 7 Fermi, Davide 7 Gao, Yu 7 Liu, Jianguo 7 Neidhardt, Hagen 7 Nizhnik, Leonid Pavlovich 7 Pilipović, Stevan 7 Rosini, Massimiliano Daniele 7 Rozovskii, Boris L. 7 Shen, Yannan 7 Song, Yongduan 7 Weikard, Rudi 7 Zhang, Tusheng S. 7 Zhou, Shouming ...and 2,608 more Authors all top 5 Cited in 403 Serials 105 Journal of Differential Equations 82 Journal of Mathematical Physics 80 Journal of Mathematical Analysis and Applications 60 Journal of Functional Analysis 53 Communications in Mathematical Physics 43 Journal of Computational Physics 43 Discrete and Continuous Dynamical Systems 34 Theoretical and Mathematical Physics 31 Nonlinear Analysis. 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