Edit Profile (opens in new tab) Karlsen, Kenneth Hvistendahl Compute Distance To: Compute Author ID: karlsen.kenneth-hvistendahl Published as: Karlsen, Kenneth H.; Karlsen, K. H.; Karlsen, Kenneth Hvistendahl; Karlsen, K. Hvistendahl; Karlsen, Kenneth Hvistendal Homepage: https://www.mn.uio.no/math/english/people/aca/kennethk/index.html External Links: MGP · ORCID · Wikidata · dblp · GND Documents Indexed: 185 Publications since 1997, including 1 Book 5 Contributions as Editor Co-Authors: 72 Co-Authors with 190 Joint Publications 1,762 Co-Co-Authors all top 5 Co-Authors 0 single-authored 46 Risebro, Nils Henrik 31 Bürger, Raimund 23 Coclite, Giuseppe Maria 22 Holden, Helge 22 Towers, John D. 17 Bendahmane, Mostafa 13 Evje, Steinar 13 Jakobsen, Espen Robstad 11 Benth, Fred Espen 11 Lie, Knut-Andreas 9 Mishra, Siddhartha 8 Reikvam, Kristin 7 Storrøsten, Erlend Briseid 6 Andreianov, Boris 6 Karper, Trygve Klovning 5 Biswas, Imran H. 4 Chen, Gui-Qiang G. 4 Dahle, Helge K. 3 Fjelde, Kjell Kåre 3 Frid, Hermano 3 Klingenberg, Christian 3 Tory, Elmer M. 3 Ulusoy, Suleyman 2 Berre, Inga 2 Berres, Stefan 2 Betancourt, Fernando 2 Brusdal, Kari 2 Cifani, Simone 2 Colombo, Rinaldo M. 2 Di Ruvo, Lorenzo 2 Galimberti, Luca 2 Hanslien, Monica 2 Hoel, Hakon A. 2 La Chioma, Claudia 2 Lagoutière, Frédéric 2 Mannseth, Trond 2 Marson, Andrea 2 Mitrovic, Darko 2 Natvig, Jostein Roald 2 Nordhaug, Hans F. 2 Tveito, Aslak 1 Amadori, Anna Lisa 1 Concha, Fernando 1 Dahl, Lars O. 1 Ding, Qian 1 Espedal, Magne S. 1 Fuchs, Franz Georg 1 Grandelius, Erik 1 Guan, Chunxia 1 Haugse, V. 1 Höfler, Kai 1 Kissling, Frederike 1 Koley, Ujjwal 1 Kwon, Young-Sam 1 Majee, Ananta K. 1 Nilssen, Trygve K. 1 Ohlberger, Mario 1 Ouaro, Stanislas 1 Pang, Peter H. C. 1 Panov, Evgeniy Yu. 1 Petitta, Francesco 1 Pierre, Charles 1 Rascle, Michel 1 Saad, Mazen 1 Tadmor, Eitan 1 Tai, Xuecheng 1 Tao, Terence 1 Torres, Héctor 1 Urbano, José Miguel 1 Wallin, Olli 1 Wendland, Wolfgang L. 1 Yin, Zhaoyang all top 5 Serials 10 Networks and Heterogeneous Media 9 Journal of Differential Equations 8 Numerische Mathematik 7 IMA Journal of Numerical Analysis 7 Mathematics of Computation 7 SIAM Journal on Numerical Analysis 6 Journal of Engineering Mathematics 6 Journal of Hyperbolic Differential Equations 5 SIAM Journal on Mathematical Analysis 5 Electronic Journal of Differential Equations (EJDE) 5 Computational Geosciences 4 Journal of Functional Analysis 4 Communications on Pure and Applied Analysis 3 Journal of Computational Physics 3 Journal of Mathematical Analysis and Applications 3 BIT 3 Finance and Stochastics 2 Archive for Rational Mechanics and Analysis 2 Applied Numerical Mathematics 2 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 2 SIAM Journal on Applied Mathematics 2 Stochastic Processes and their Applications 2 Stochastics and Stochastics Reports 2 Advances in Differential Equations 2 Discrete and Continuous Dynamical Systems 2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 2 International Journal of Theoretical and Applied Finance 2 Interfaces and Free Boundaries 2 Acta Mathematica Scientia. Series B. (English Edition) 2 Communications in Mathematical Sciences 2 International Journal of Numerical Analysis and Modeling 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 Bollettino dell’Unione Matematica Italiana. Series IX 1 Computers and Fluids 1 Computers & Mathematics with Applications 1 Computer Methods in Applied Mechanics and Engineering 1 Nonlinearity 1 Applied Mathematics and Optimization 1 Journal of Computational and Applied Mathematics 1 Nonlinear Analysis. 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Analysis and Computations 1 EMS Series of Lectures in Mathematics all top 5 Fields 146 Partial differential equations (35-XX) 85 Numerical analysis (65-XX) 58 Fluid mechanics (76-XX) 14 Probability theory and stochastic processes (60-XX) 14 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 13 Calculus of variations and optimal control; optimization (49-XX) 10 Biology and other natural sciences (92-XX) 9 Integral equations (45-XX) 9 Mechanics of deformable solids (74-XX) 7 Geophysics (86-XX) 6 Systems theory; control (93-XX) 5 General and overarching topics; collections (00-XX) 4 Operations research, mathematical programming (90-XX) 3 Operator theory (47-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Mechanics of particles and systems (70-XX) 2 Optics, electromagnetic theory (78-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Functional analysis (46-XX) 1 Classical thermodynamics, heat transfer (80-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 172 Publications have been cited 2,966 times in 1,593 Documents Cited by ▼ Year ▼ On the well-posedness of the Degasperis-Procesi equation. Zbl 1090.35142Coclite, Giuseppe M.; Karlsen, Kenneth H. 131 2006 Global weak solutions to a generalized hyperelastic-rod wave equation. Zbl 1100.35106Coclite, G. M.; Holden, H.; Karlsen, K. H. 84 2005 A theory of \(L ^{1}\)-dissipative solvers for scalar conservation laws with discontinuous flux. Zbl 1261.35088Andreianov, Boris; Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik 74 2011 Strongly degenerate parabolic-hyperbolic systems modeling polydisperse sedimentation with compression. Zbl 1047.35071Berres, Stefan; Bürger, Raimund; Karlsen, Kenneth H.; Tory, Elmer M. 67 2003 \(L^1\) stability for entropy solutions of nonlinear degenerate parabolic convection-diffusion equations with discontinuous coefficients. Zbl 1036.35104Karlsen, K. H.; Risebro, N. H.; Towers, J. D. 66 2003 On the uniqueness and stability of entropy solutions of nonlinear degenerate parabolic equations with rough coefficients. Zbl 1027.35057Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik 64 2003 Global existence of weak solutions for a viscous two-phase model. Zbl 1148.76056Evje, Steinar; Karlsen, Kenneth H. 63 2008 Wellposedness for a parabolic-elliptic system. Zbl 1082.35056Coclite, Giuseppe Maria; Holden, Helge; Karlsen, Kenneth Hvistendahl 61 2005 Convergence of the Lax-Friedrichs scheme and stability for conservation laws with a discontinuous space-time dependent flux. Zbl 1112.65085Karlsen, K. H.; Towers, J. D. 58 2004 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 57 2010 Upwind difference approximations for degenerate parabolic convection-diffusion equations with a discontinuous coefficient. Zbl 1014.65073Karlsen, K. H.; Risebro, N. H.; Towers, J. D. 56 2002 Well-posedness in \(BV_t\) and convergence of a difference scheme for continuous sedimentation in ideal clarifier-thickener units. Zbl 1053.76047Bürger, R.; Karlsen, K. H.; Risebro, N. H.; Towers, J. D. 53 2004 On nonlinear stochastic balance laws. Zbl 1261.60062Chen, Gui-Qiang; Ding, Qian; Karlsen, Kenneth H. 50 2012 A “maximum principle for semicontinuous functions” applicable to integro-partial differential equations. Zbl 1105.45006Jakobsen, Espen R.; Karlsen, Kenneth H. 49 2006 An Engquist-Osher-type scheme for conservation laws with discontinuous flux adapted to flux connections. Zbl 1201.35022Bürger, Raimund; Karlsen, Kenneth H.; Towers, John D. 47 2009 Continuous dependence estimates for viscosity solutions of integro-PDEs. Zbl 1082.45008Jakobsen, Espen R.; Karlsen, Kenneth H. 45 2005 On nonlocal conservation laws modelling sedimentation. Zbl 1381.76368Betancourt, F.; Bürger, R.; Karlsen, K. H.; Tory, E. M. 43 2011 Global weak solutions for a viscous liquid-gas model with singular pressure law. Zbl 1175.76143Evje, Steinar; Karlsen, Kenneth Hvistendahl 40 2009 Optimal portfolio selection with consumption and nonlinear integro-differential equations with gradient constraint: A viscosity solution approach. Zbl 0978.91039Benth, Fred Espen; Karlsen, Kenneth Hvistendahl; Reikvam, Kristin 40 2001 Monotone difference approximations of BV solutions to degenerate convection-diffusion equations. Zbl 0985.65100Evje, Steinar; Karlsen, Kenneth Hvistendahl 40 2000 Analysis of a class of degenerate reaction-diffusion systems and the bidomain model of cardiac tissue. Zbl 1179.35162Bendahmane, Mostafa; Karlsen, Kenneth H. 40 2006 Well-posedness and blow-up phenomena for a modified two-component Camassa-Holm equation. Zbl 1213.35133Guan, Chunxia; Karlsen, Kenneth H.; Yin, Zhaoyang 38 2010 Renormalized solutions of an anisotropic reaction-diffusion-advection system with \(L^1\) data. Zbl 1134.35371Bendahmane, Mostafa; Karlsen, Kenneth H. 37 2006 Renormalized entropy solutions for quasi-linear anisotropic degenerate parabolic equations. Zbl 1090.35104Bendahmane, Mostafa; Karlsen, Kenneth H. 36 2004 A model of continuous sedimentation of flocculated suspensions in clarifier-thickener units. Zbl 1089.76061Bürger, Raimund; Karlsen, Kenneth H.; Towers, John D. 35 2005 Quasilinear anisotropic degenerate parabolic equations with time-space dependent diffusion coefficients. Zbl 1084.35034Chen, Gui-Qiang; Karlsen, Kenneth H. 34 2005 Operator splitting for the KdV equation. Zbl 1219.35235Holden, Helge; Karlsen, Kenneth H.; Risebro, Nils Henrik; Tao, Terence 33 2011 A family of numerical schemes for kinematic flows with discontinuous flux. Zbl 1200.76126Bürger, R.; García, A.; Karlsen, K. H.; Towers, J. D. 33 2008 Convergence of finite difference schemes for viscous and inviscid conservation laws with rough coefficients. Zbl 1032.76048Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik 32 2001 Well-posedness of higher-order Camassa-Holm equations. Zbl 1186.35003Coclite, G. M.; Holden, H.; Karlsen, K. H. 30 2009 Numerical schemes for computing discontinuous solutions of the Degasperis-Procesi equation. Zbl 1246.76114Coclite, G. M.; Karlsen, K. H.; Risebro, N. H. 29 2008 Numerical solution of reservoir flow models based on large time step operator splitting algorithms. Zbl 1077.76546Espedal, Magne S.; Karlsen, Kenneth Hvistendahl 28 2000 Discrete duality finite volume schemes for doubly nonlinear degenerate hyperbolic-parabolic equations. Zbl 1207.35020Andreianov, B.; Bendahmane, M.; Karlsen, K. H. 28 2010 On vanishing viscosity approximation of conservation laws with discontinuous flux. Zbl 1270.35305Andreianov, Boris; Karlsen, Kenneth H.; Risebro, Nils H. 27 2010 On strongly degenerate convection-diffusion problems modeling sedimentation-consolidation processes. Zbl 0961.35078Bürger, R.; Evje, S.; Karlsen, K. Hvistendahl 26 2000 Well-posedness results for triply nonlinear degenerate parabolic equations. Zbl 1178.35212Andreianov, B.; Bendahmane, M.; Karlsen, K. H.; Ouaro, S. 25 2009 A front tracking approach to a model of continuous sedimentation in ideal clarifier-thickener units. Zbl 1013.35052Bürger, R.; Karlsen, K. H.; Klingenberg, C.; Risebro, N. H. 25 2003 Merton’s portfolio optimization problem in a Black and Scholes market with non-Gaussian stochastic volatility of Ornstein-Uhlenbeck type. Zbl 1049.91060Benth, Fred Espen; Karlsen, Kenneth Hvistendahl; Reikvam, Kristin 25 2003 Operator splitting methods for generalized Korteweg-de Vries equations. Zbl 0947.65102Holden, Helge; Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik 24 1999 A singular limit problem for conservation laws related to the Camassa–Holm shallow water equation. Zbl 1102.35010Coclite, Giuseppe Maria; Karlsen, Kenneth Hvistendahl 24 2006 On the uniqueness of discontinuous solutions to the Degasperis-Procesi equation. Zbl 1133.35028Coclite, Giuseppe M.; Karlsen, Kenneth H. 23 2007 A duality approach to the fractional Laplacian with measure data. Zbl 1208.35162Karlsen, Kenneth H.; Petitta, Francesco; Ulusoy, Suleyman 23 2011 Initial-boundary value problems for conservation laws with source terms and the Degasperis-Procesi equation. Zbl 1180.35348Coclite, G. M.; Karlsen, K. H.; Kwon, Y.-S. 22 2009 Operator splitting methods for systems of convection-diffusion equations: nonlinear error mechanisms and correction strategies. Zbl 1051.76046Karlsen, K. Hvistendahl; Lie, K.-A.; Natvig, J. R.; Nordhaug, H. F.; Dahle, H. K. 22 2001 An operator splitting method for nonlinear convection-diffusion equations. Zbl 0882.35074Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik 22 1997 An unconditionally stable splitting scheme for a class of nonlinear parabolic equations. Zbl 0949.65089Karlsen, Kenneth Hvistendahl; Lie, Knut-Andreas 21 1999 Continuous dependence estimates for viscosity solutions of fully nonlinear degenerate parabolic equations. Zbl 1086.35061Jakobsen, Espen R.; Karlsen, Kenneth H. 21 2002 On a two-sidedly degenerate chemotaxis model with volume-filling effect. Zbl 1133.35061Bendahmane, Mostafa; Karlsen, Kenneth H.; Urbano, José Miguel 21 2007 A convergent finite difference scheme for the Camassa–Holm equation with general \(H^1\) initial data. Zbl 1172.35310Coclite, G. M.; Karlsen, K. H.; Risebro, N. H. 20 2008 Nonlinear anisotropic elliptic and parabolic equations in \(\mathbb R^{N}\) with advection and lower order terms and locally integrable data. Zbl 1087.35035Bendahmane, Mostafa; Karlsen, Kenneth H. 20 2005 On the well-posedness of entropy solutions to conservation laws with a zero-flux boundary condition. Zbl 1160.35048Bürger, Raimund; Frid, Hermano; Karlsen, Kenneth H. 20 2007 Viscosity solutions for a system of integro-PDEs and connections to optimal switching and control of jump-diffusion processes. Zbl 1197.49028Biswas, Imran H.; Jakobsen, Espen R.; Karlsen, Kenneth H. 20 2010 \(L^1\)-framework for continuous dependence and error estimates for quasilinear anisotropic degenerate parabolic equations. Zbl 1096.35072Chen, Gui-Qiang; Karlsen, Kenneth H. 20 2006 Some wellposedness results for the Ostrovsky-Hunter equation. Zbl 1284.35131Coclite, G. M.; Di Ruvo, L.; Karlsen, K. H. 19 2014 A note on Merton’s portfolio selection problem for the Schwartz mean-reversion model. Zbl 1074.60068Benth, Fred Espen; Karlsen, Kenneth Hvistendahl 19 2005 On a nonlinear degenerate parabolic transport-diffusion equation with a discontinuous coefficient. Zbl 1015.35049Karlsen, Kenneth H.; Risebro, Nils H.; Towers, John D. 18 2002 Optimal portfolio management rules in a non-Gaussian market with durability and intertemporal substitution. Zbl 1049.91059Benth, Fred Espen; Karlsen, Kenneth Hvistendahl; Reikvam, Kristin 18 2001 Portfolio optimization in a Lévy market with intertemporal substitution and transaction costs. Zbl 1035.91027Benth, Fred Espen; Karlsen, Kenneth Hvistendahl; Reikvam, Kristin 18 2002 High-resolution hybrid primitive-conservative upwind schemes for the drift flux model. Zbl 1059.76044Fjelde, Kjell Kåre; Karlsen, Kenneth Hvistendahl 17 2002 A note on the uniqueness of entropy solutions of nonlinear degenerate parabolic equations. Zbl 1072.35545Karlsen, Kenneth H.; Ohlberger, Mario 17 2002 On a diffusively corrected kinematic-wave traffic flow model with changing road surface conditions. Zbl 1055.35071Bürger, R.; Karlsen, K. H. 17 2003 A note on front tracking and the equivalence between viscosity solutions of Hamilton-Jacobi equations and entropy solutions of scalar conservation laws. Zbl 1010.35026Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik 16 2002 Model equations and instability regions for the sedimentation of polydisperse suspensions of spheres. Zbl 1011.35017Bürger, R.; Karlsen, K. H.; Tory, E. M.; Wendland, W. L. 16 2002 The corrected operator splitting approach applied to a nonlinear advection-diffusion problem. Zbl 0942.76047Karlsen, K. Hvistendahl; Brusdal, K.; Dahle, H. K.; Evje, S.; Lie, K.-A. 15 1998 Stable upwind schemes for the magnetic induction equation. Zbl 1177.78057Fuchs, Franz G.; Karlsen, Kenneth H.; Mishra, Siddharta; Risebro, Nils H. 15 2009 The discontinuous Galerkin method for fractional degenerate convection-diffusion equations. Zbl 1247.65128Cifani, Simone; Jakobsen, Espen R.; Karlsen, Kenneth H. 15 2011 Convergent difference schemes for the Hunter–Saxton equation. Zbl 1114.65101Holden, H.; Karlsen, K. H.; Risebro, N. H. 15 2007 Difference-quadrature schemes for nonlinear degenerate parabolic integro-PDE. Zbl 1218.65147Biswas, Imran H.; Jakobsen, Espen R.; Karlsen, Kenneth H. 14 2010 On the convergence rate of operator splitting for Hamilton-Jacobi equations with source terms. Zbl 1059.70012Jakobsen, Espen Robstad; Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik 14 2001 Central difference solutions of the kinematic model of settling of polydisperse suspensions and three-dimensional particle-scale simulations. Zbl 1014.76060Bürger, R.; Fjelde, K.-K.; Höfler, K.; Karlsen, K. Hvistendahl 14 2001 On the existence and compactness of a two-dimensional resonant system of conservation laws. Zbl 1165.35412Karlsen, Kenneth H.; Rascle, Michel; Tadmor, Eitan 14 2007 Monotone difference approximations for the simulation of clarifier-thickener units. Zbl 1299.76283Bürger, R.; Karlsen, K. H.; Risebro, N. H.; Towers, J. D. 14 2004 A semilinear Black and Scholes partial differential equation for valuing American options. Zbl 1064.60080Benth, Fred E.; Karlsen, Kenneth H.; Reikvam, Kristin 14 2003 Difference schemes, entropy solutions, and speedup impulse for an inhomogeneous kinematic traffic flow model. Zbl 1173.35586Bürger, Raimund; García, Antonio; Karlsen, Kenneth H.; Towers, John D. 14 2008 Corrected operator splitting for nonlinear parabolic equations. Zbl 0951.35080Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik 13 2000 The discontinuous Galerkin method for fractal conservation laws. Zbl 1256.65089Cifani, Simone; Jakobsen, Espen R.; Karlsen, Kenneth H. 13 2011 Continuous dependence estimates for viscosity solutions of fully nonlinear degenerate elliptic equations. Zbl 1010.35050Jakobsen, Espen R.; Karlsen, Kenneth H. 13 2002 Central schemes and systems of conservation laws with discontinuous coefficients modeling gravity separation of polydisperse suspensions. Zbl 1107.76366Berres, S.; Bürger, R.; Karlsen, K. H. 13 2004 Error estimates for approximate solutions to Bellman equations associated with controlled jump-diffusions. Zbl 1153.65125Jakobsen, Espen R.; Karlsen, Kenneth H.; La Chioma, Claudia 13 2008 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 Convergence of finite volume schemes for triangular systems of conservation laws. Zbl 1190.65133Karlsen, Kenneth Hvistendahl; Mishra, Siddhartha; Risebro, Nils Henrik 11 2009 Conservation laws driven by Lévy white noise. Zbl 1333.35357Biswas, Imran H.; Karlsen, Kenneth H.; Majee, Ananta K. 11 2015 Anisotropic nonlinear elliptic systems with measure data and anisotropic harmonic maps into spheres. Zbl 1128.35039Bendahmane, Mostafa; Karlsen, Kenneth H. 11 2006 On stochastic conservation laws and Malliavin calculus. Zbl 1354.60070Karlsen, K. H.; Storrøsten, E. B. 11 2017 Convergence of discrete duality finite volume schemes for the cardiac bidomain model. Zbl 1328.65190Andreianov, Boris; Bendahmane, Mostafa; Karlsen, Kenneth H.; Pierre, Charles 11 2011 A PDE representation of the density of the minimal entropy martingale measure in stochastic volatility markets. Zbl 1115.91025Benth, Fred Espen; Karlsen, Kenneth Hvistendahl 11 2005 An error estimate for the finite difference approximation to degenerate convection-diffusion equations. Zbl 1248.65098Karlsen, K. H.; Koley, U.; Risebro, N. H. 11 2012 Periodic solutions of the Degasperis-Procesi equation: well-posedness and asymptotics. Zbl 1316.35081Coclite, G. M.; Karlsen, K. H. 10 2015 A relaxation scheme for continuous sedimentation in ideal clarifier-thickener units. Zbl 1122.76063Bürger, R.; Karlsen, K. H.; Risebro, N. H. 10 2005 A relaxation scheme for conservation laws with a discontinuous coefficient. Zbl 1078.65076Karlsen, K. H.; Klingenberg, C.; Risebro, N. H. 10 2004 Conservation laws with discontinuous flux: a short introduction. Zbl 1138.35365Bürger, Raimund; Karlsen, Kenneth H. 10 2008 Uniqueness of entropy solutions for doubly nonlinear anisotropic degenerate parabolic equations. Zbl 1090.35105Bendahmane, Mostafa; Karlsen, Kenneth H. 10 2005 Unconditionally stable methods for Hamilton-Jacobi equations. Zbl 1143.65365Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik 10 2002 A convergent mixed method for the Stokes approximation of viscous compressible flow. Zbl 1427.76131Karlsen, Kenneth H.; Karper, Trygve K. 10 2012 Nonlinear anisotropic elliptic and parabolic equations with variable exponents and \(L^1\) data. Zbl 1268.35053Bendahmane, Mostafa; Karlsen, Kenneth Hvistendahl; Saad, Mazen 9 2013 Identification of diffusion parameters in a nonlinear convection-diffusion equation using the augmented Lagrangian method. Zbl 1179.65122Nilssen, T. K.; Karlsen, K. H.; Mannseth, T.; Tai, X.-C. 9 2009 Convergence of a Godunov scheme for conservation laws with a discontinuous flux lacking the crossing condition. Zbl 1380.65158Karlsen, K. H.; Towers, J. D. 9 2017 An explicit finite difference scheme for the Camassa-Holm equation. Zbl 1191.35021Coclite, Giuseppe Maria; Karlsen, Kenneth H.; Risebro, Nils Henrik 9 2008 \(L^{1}\) error estimates for difference approximations of degenerate convection-diffusion equations. Zbl 1300.65067Karlsen, K. H.; Risebro, N. H.; Storrøsten, E. B. 9 2014 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. 9 2003 The Hunter-Saxton equation with noise. Zbl 1451.35266Holden, Helge; Karlsen, Kenneth H.; Pang, Peter H. C. 1 2021 Numerical methods for conservation laws with rough flux. Zbl 1437.35485Hoel, H.; Karlsen, K. H.; Risebro, N. H.; Storrøsten, E. B. 2 2020 The Cardiac bidomain model and homogenization. Zbl 1423.35200Grandelius, Erik; Karlsen, Kenneth H. 5 2019 Well-posedness theory for stochastically forced conservation laws on Riemannian manifolds. Zbl 1437.35482Galimberti, L.; Karlsen, K. H. 2 2019 The initial-boundary-value problem for an Ostrovsky-Hunter type equation. Zbl 1402.35086Coclite, Giuseppe Maria; di Ruvo, Lorenzo; Karlsen, Kenneth Hvistendahl 5 2018 Analysis of a splitting method for stochastic balance laws. Zbl 1475.65153Karlsen, K. H.; Storrøsten, E. B. 5 2018 Path-dependent convex conservation laws. Zbl 1402.35170Hoel, H.; Karlsen, K. H.; Risebro, N. H.; Storrøsten, E. B. 4 2018 On stochastic conservation laws and Malliavin calculus. Zbl 1354.60070Karlsen, K. H.; Storrøsten, E. B. 11 2017 Convergence of a Godunov scheme for conservation laws with a discontinuous flux lacking the crossing condition. Zbl 1380.65158Karlsen, K. H.; Towers, J. D. 9 2017 Practical convergence rates for degenerate parabolic equations. Zbl 1372.35166Karlsen, Kenneth H.; Risebro, Nils H.; Storrøsten, E. B. 1 2017 Convergence of monotone schemes for conservation laws with zero-flux boundary conditions. Zbl 07407140Karlsen, K. H.; Towers, J. D. 1 2017 On the convergence rate of finite difference methods for degenerate convection-diffusion equations in several space dimensions. Zbl 1342.65182Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik; Storrøsten, Erlend Briseid 5 2016 On a hyperbolic Keller-Segel system with degenerate nonlinear fractional diffusion. Zbl 1348.35289Karlsen, Kenneth H.; Ulusoy, Süleyman 2 2016 Conservation laws driven by Lévy white noise. Zbl 1333.35357Biswas, Imran H.; Karlsen, Kenneth H.; Majee, Ananta K. 11 2015 Periodic solutions of the Degasperis-Procesi equation: well-posedness and asymptotics. Zbl 1316.35081Coclite, G. M.; Karlsen, K. H. 10 2015 A note on the Camassa-Holm equation. Zbl 1316.35082Coclite, G. M.; Karlsen, K. H. 5 2015 Some wellposedness results for the Ostrovsky-Hunter equation. Zbl 1284.35131Coclite, G. M.; Di Ruvo, L.; Karlsen, K. H. 19 2014 \(L^{1}\) error estimates for difference approximations of degenerate convection-diffusion equations. Zbl 1300.65067Karlsen, K. H.; Risebro, N. H.; Storrøsten, E. B. 9 2014 On the singular limit of a two-phase flow equation with heterogeneities and dynamic capillary pressure. Zbl 1297.76163Kissling, Frederike; Karlsen, Kenneth H. 4 2014 Nonlinear anisotropic elliptic and parabolic equations with variable exponents and \(L^1\) data. Zbl 1268.35053Bendahmane, Mostafa; Karlsen, Kenneth Hvistendahl; Saad, Mazen 9 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 On nonlinear stochastic balance laws. Zbl 1261.60062Chen, Gui-Qiang; Ding, Qian; Karlsen, Kenneth H. 50 2012 An error estimate for the finite difference approximation to degenerate convection-diffusion equations. Zbl 1248.65098Karlsen, K. H.; Koley, U.; Risebro, N. H. 11 2012 A convergent mixed method for the Stokes approximation of viscous compressible flow. Zbl 1427.76131Karlsen, Kenneth H.; Karper, Trygve K. 10 2012 A hyperbolic-elliptic model of two-phase flow in porous media-existence of entropy solutions. Zbl 1277.76100Coclite, G. M.; Karlsen, K. H.; Mishra, S.; Risebro, N. H. 5 2012 A note on entropy solutions for degenerate parabolic equations with \(L^1 \cap L^p\) data. Zbl 1255.35141Bendahmane, Mostafa; Karlsen, Kenneth Hvistendahl 1 2012 Analysis of a compressible gas-liquid model motivated by oil well control operations. Zbl 1265.76094Evje, Steinar; Karlsen, K. H. 1 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 On an initial-boundary value problem for the hyperelastic rod wave equation. Zbl 1252.35131Coclite, Giuseppe Maria; Karlsen, Kenneth Hvistendahl 1 2012 A theory of \(L ^{1}\)-dissipative solvers for scalar conservation laws with discontinuous flux. Zbl 1261.35088Andreianov, Boris; Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik 74 2011 On nonlocal conservation laws modelling sedimentation. Zbl 1381.76368Betancourt, F.; Bürger, R.; Karlsen, K. H.; Tory, E. M. 43 2011 Operator splitting for the KdV equation. Zbl 1219.35235Holden, Helge; Karlsen, Kenneth H.; Risebro, Nils Henrik; Tao, Terence 33 2011 A duality approach to the fractional Laplacian with measure data. Zbl 1208.35162Karlsen, Kenneth H.; Petitta, Francesco; Ulusoy, Suleyman 23 2011 The discontinuous Galerkin method for fractional degenerate convection-diffusion equations. Zbl 1247.65128Cifani, Simone; Jakobsen, Espen R.; Karlsen, Kenneth H. 15 2011 The discontinuous Galerkin method for fractal conservation laws. Zbl 1256.65089Cifani, Simone; Jakobsen, Espen R.; Karlsen, Kenneth H. 13 2011 Convergence of discrete duality finite volume schemes for the cardiac bidomain model. Zbl 1328.65190Andreianov, Boris; Bendahmane, Mostafa; Karlsen, Kenneth H.; Pierre, Charles 11 2011 Stability of entropy solutions for Lévy mixed hyperbolic-parabolic equations. Zbl 1270.35084Karlsen, Kenneth H.; Ulusoy, Suleyman 8 2011 Convergence of a mixed method for a semi-stationary compressible Stokes system. Zbl 1219.65094Karlsen, Kenneth H.; Karper, Trygve K. 7 2011 A strongly degenerate parabolic aggregation equation. Zbl 1272.35125Betancourt, F.; Bürger, R.; Karlsen, K. H. 5 2011 \(L^\infty\) solutions for a model of nonisothermal polytropic gas flow. Zbl 1252.35197Frid, Hermano; Holden, Helge; Karlsen, Kenneth H. 1 2011 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 57 2010 Well-posedness and blow-up phenomena for a modified two-component Camassa-Holm equation. Zbl 1213.35133Guan, Chunxia; Karlsen, Kenneth H.; Yin, Zhaoyang 38 2010 Discrete duality finite volume schemes for doubly nonlinear degenerate hyperbolic-parabolic equations. Zbl 1207.35020Andreianov, B.; Bendahmane, M.; Karlsen, K. H. 28 2010 On vanishing viscosity approximation of conservation laws with discontinuous flux. Zbl 1270.35305Andreianov, Boris; Karlsen, Kenneth H.; Risebro, Nils H. 27 2010 Viscosity solutions for a system of integro-PDEs and connections to optimal switching and control of jump-diffusion processes. Zbl 1197.49028Biswas, Imran H.; Jakobsen, Espen R.; Karlsen, Kenneth H. 20 2010 Difference-quadrature schemes for nonlinear degenerate parabolic integro-PDE. Zbl 1218.65147Biswas, Imran H.; Jakobsen, Espen R.; Karlsen, Kenneth H. 14 2010 Second-order schemes for conservation laws with discontinuous flux modelling clarifier-thickener units. Zbl 1204.65101Bürger, Raimund; Karlsen, Kenneth H.; Torres, Héctor; Towers, John D. 9 2010 A convergent nonconforming finite element method for compressible Stokes flow. Zbl 1222.35141Karlsen, Kenneth H.; Karper, Trygve K. 7 2010 On some difference schemes and entropy conditions for a class of multi-species kinematic flow models with discontinuous flux. Zbl 1263.76048Bürger, Raimund; Karlsen, Kenneth H.; Towers, John D. 6 2010 An Engquist-Osher-type scheme for conservation laws with discontinuous flux adapted to flux connections. Zbl 1201.35022Bürger, Raimund; Karlsen, Kenneth H.; Towers, John D. 47 2009 Global weak solutions for a viscous liquid-gas model with singular pressure law. Zbl 1175.76143Evje, Steinar; Karlsen, Kenneth Hvistendahl 40 2009 Well-posedness of higher-order Camassa-Holm equations. Zbl 1186.35003Coclite, G. M.; Holden, H.; Karlsen, K. H. 30 2009 Well-posedness results for triply nonlinear degenerate parabolic equations. Zbl 1178.35212Andreianov, B.; Bendahmane, M.; Karlsen, K. H.; Ouaro, S. 25 2009 Initial-boundary value problems for conservation laws with source terms and the Degasperis-Procesi equation. Zbl 1180.35348Coclite, G. M.; Karlsen, K. H.; Kwon, Y.-S. 22 2009 Stable upwind schemes for the magnetic induction equation. Zbl 1177.78057Fuchs, Franz G.; Karlsen, Kenneth H.; Mishra, Siddharta; Risebro, Nils H. 15 2009 Convergence of finite volume schemes for triangular systems of conservation laws. Zbl 1190.65133Karlsen, Kenneth Hvistendahl; Mishra, Siddhartha; Risebro, Nils Henrik 11 2009 Identification of diffusion parameters in a nonlinear convection-diffusion equation using the augmented Lagrangian method. Zbl 1179.65122Nilssen, T. K.; Karlsen, K. H.; Mannseth, T.; Tai, X.-C. 9 2009 A convergent finite-difference method for a nonlinear variational wave equation. Zbl 1236.65112Holden, H.; Karlsen, K. H.; Risebro, N. H. 8 2009 Convergence of a finite volume scheme for the bidomain model of cardiac tissue. Zbl 1165.92005Bendahmane, Mostafa; Karlsen, Kenneth H. 7 2009 Well-balanced schemes for conservation laws with source terms based on a local discontinuous flux formulation. Zbl 1198.35149Karlsen, Kenneth Hvistendahl; Mishra, Siddhartha; Risebro, Nils Henrik 6 2009 Convergence of vanishing viscosity approximations of \(2\times 2\) triangular systems of multi-dimensional conservation laws. Zbl 1178.35246Coclite, G. M.; Karlsen, K. H.; Mishra, S.; Risebro, N. H. 5 2009 Semi-Godunov schemes for multiphase flows in porous media. Zbl 1191.35022Karlsen, K. H.; Mishra, S.; Risebro, N. H. 5 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. 4 2009 A conservation law with discontinuous flux modelling traffic flow with abruptly changing road surface conditions. Zbl 1186.35005Bürger, Raimund; Karlsen, Kenneth H.; Towers, John D. 3 2009 Zero diffusion-dispersion-smoothing limits for a scalar conservation law with discontinuous flux function. Zbl 1206.35170Holden, H.; Karlsen, K. H.; Mitrovic, D. 2 2009 A semilinear equation for the American option in a general jump market. Zbl 1182.91218Karlsen, Kenneth H.; Wallin, Olli 1 2009 Global existence of weak solutions for a viscous two-phase model. Zbl 1148.76056Evje, Steinar; Karlsen, Kenneth H. 63 2008 A family of numerical schemes for kinematic flows with discontinuous flux. Zbl 1200.76126Bürger, R.; García, A.; Karlsen, K. H.; Towers, J. D. 33 2008 Numerical schemes for computing discontinuous solutions of the Degasperis-Procesi equation. Zbl 1246.76114Coclite, G. M.; Karlsen, K. H.; Risebro, N. H. 29 2008 A convergent finite difference scheme for the Camassa–Holm equation with general \(H^1\) initial data. Zbl 1172.35310Coclite, G. M.; Karlsen, K. H.; Risebro, N. H. 20 2008 Difference schemes, entropy solutions, and speedup impulse for an inhomogeneous kinematic traffic flow model. Zbl 1173.35586Bürger, Raimund; García, Antonio; Karlsen, Kenneth H.; Towers, John D. 14 2008 Error estimates for approximate solutions to Bellman equations associated with controlled jump-diffusions. Zbl 1153.65125Jakobsen, Espen R.; Karlsen, Kenneth H.; La Chioma, Claudia 13 2008 Conservation laws with discontinuous flux: a short introduction. Zbl 1138.35365Bürger, Raimund; Karlsen, Kenneth H. 10 2008 An explicit finite difference scheme for the Camassa-Holm equation. Zbl 1191.35021Coclite, Giuseppe Maria; Karlsen, Kenneth H.; Risebro, Nils Henrik 9 2008 Bounded solutions for the Degasperis-Procesi equation. Zbl 1164.35071Coclite, Giuseppe Maria; Karlsen, Kenneth H. 5 2008 Error estimates for a class of finite difference-quadrature schemes for fully nonlinear degenerate parabolic integro-PDEs. Zbl 1170.65102Biswas, Imran H.; Jakobsen, Espen R.; Karlsen, Kenneth H. 4 2008 A gradient reconstruction formula for finite volume schemes and discrete duality. Zbl 1422.65200Andreianov, Boris; Bendahmane, Mostafa; Karlsen, Kenneth H. 2 2008 A hyperbolic-elliptic model for coupled well-porous media flow. Zbl 1388.35154Evje, S.; Karlsen, K. H. 2 2008 Global weak solutions for a shallow water equation. Zbl 1168.35415Coclite, G. M.; Holden, H.; Karlsen, K. H. 1 2008 Semi-Godunov schemes for general triangular systems of conservation laws. Zbl 1133.76033Karlsen, Kenneth Hvistendahl; Mishra, Siddhartha; Risebro, Nils Henrik 1 2008 Discontinuous solutions for the Degasperis-Procesi equation. Zbl 1157.35455Coclite, G. M.; Karlsen, K. H. 1 2008 On the uniqueness of discontinuous solutions to the Degasperis-Procesi equation. Zbl 1133.35028Coclite, Giuseppe M.; Karlsen, Kenneth H. 23 2007 On a two-sidedly degenerate chemotaxis model with volume-filling effect. Zbl 1133.35061Bendahmane, Mostafa; Karlsen, Kenneth H.; Urbano, José Miguel 21 2007 On the well-posedness of entropy solutions to conservation laws with a zero-flux boundary condition. Zbl 1160.35048Bürger, Raimund; Frid, Hermano; Karlsen, Kenneth H. 20 2007 Convergent difference schemes for the Hunter–Saxton equation. Zbl 1114.65101Holden, H.; Karlsen, K. H.; Risebro, N. H. 15 2007 On the existence and compactness of a two-dimensional resonant system of conservation laws. Zbl 1165.35412Karlsen, Kenneth H.; Rascle, Michel; Tadmor, Eitan 14 2007 Error estimates for finite difference-quadrature schemes for a class of nonlocal Bellman equations with variable diffusion. Zbl 1125.65362Biswas, Imran H.; Jakobsen, Espen R.; Karlsen, Kenneth H. 2 2007 On the well-posedness of the Degasperis-Procesi equation. Zbl 1090.35142Coclite, Giuseppe M.; Karlsen, Kenneth H. 131 2006 A “maximum principle for semicontinuous functions” applicable to integro-partial differential equations. Zbl 1105.45006Jakobsen, Espen R.; Karlsen, Kenneth H. 49 2006 Analysis of a class of degenerate reaction-diffusion systems and the bidomain model of cardiac tissue. Zbl 1179.35162Bendahmane, Mostafa; Karlsen, Kenneth H. 40 2006 Renormalized solutions of an anisotropic reaction-diffusion-advection system with \(L^1\) data. Zbl 1134.35371Bendahmane, Mostafa; Karlsen, Kenneth H. 37 2006 A singular limit problem for conservation laws related to the Camassa–Holm shallow water equation. Zbl 1102.35010Coclite, Giuseppe Maria; Karlsen, Kenneth Hvistendahl 24 2006 \(L^1\)-framework for continuous dependence and error estimates for quasilinear anisotropic degenerate parabolic equations. Zbl 1096.35072Chen, Gui-Qiang; Karlsen, Kenneth H. 20 2006 Anisotropic nonlinear elliptic systems with measure data and anisotropic harmonic maps into spheres. Zbl 1128.35039Bendahmane, Mostafa; Karlsen, Kenneth H. 11 2006 On an extended clarifier-thickener model with singular source and sink terms. Zbl 1201.35130Bürger, R.; Garcia, A.; Karlsen, K. H.; Towers, J. D. 5 2006 On a finite difference scheme for a Beeler-Reuter based model of cardiac electrical activity. Zbl 1162.92312Hanslien, Monica; Karlsen, Kenneth H.; Tveito, Aslak 2 2006 \(H^1\)-Perturbations of smooth solutions for a weakly dissipative hyperelastic-rod wave equation. Zbl 1167.35463Coclite, Giuseppe Maria; Bendahmane, Mostafa; Karlsen, Kenneth H. 2 2006 A semigroup of solutions for the Degasperis-Procesi equation. Zbl 1345.35123Coclite, G. M.; Karlsen, K. H. 1 2006 Hyperbolic-elliptic models for well-reservoir flow. Zbl 1119.35035Evje, Steinar; Karlsen, Kenneth H. 1 2006 ...and 72 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,900 Authors 68 Karlsen, Kenneth Hvistendahl 57 Coclite, Giuseppe Maria 52 Bürger, Raimund 46 Yin, Zhaoyang 43 Risebro, Nils Henrik 32 Bendahmane, Mostafa 31 Andreianov, Boris 27 Di Ruvo, Lorenzo 24 Holden, Helge 22 Jakobsen, Espen Robstad 20 Goatin, Paola 20 Lai, Shaoyong 18 Mishra, Siddhartha 17 Evje, Steinar 17 Zhan, Huashui 15 Wen, Huanyao 14 Liu, Yue 14 Ruiz-Baier, Ricardo 13 Mulet, Pep 13 Towers, John D. 12 Diehl, Stefan 12 Raynaud, Xavier 12 Saad, Mazen 11 Koley, Ujjwal 11 Shangerganesh, Lingeshwaran 11 Tian, Lixin 11 Villada, Luis Miguel 11 Yao, Lei 11 Zhu, Changjiang 10 Wittbold, Petra 9 Abreu, Eduardo 9 Balachandran, Krishnan 9 Biswas, Imran H. 9 Gowda, G. D. Veerappa 9 Grunert, Katrin 9 Guo, Zhengguang 9 Kwon, Young-Sam 9 Liu, Hailiang 9 Wu, Xinglong 9 Yan, Kai 8 Adimurthi, A. 8 Cancès, Clément 8 Chen, Gui-Qiang G. 8 Colombo, Rinaldo M. 8 Gao, Hongjun 8 Gess, Benjamin 8 Lv, Guangying 8 Mokhtari, Fares 8 Panov, Evgeniy Yu. 8 Rosini, Massimiliano Daniele 8 Sepúlveda, Mauricio A. 8 Zhang, Yinghui 7 Bauzet, Caroline 7 Geiser, Jürgen 7 Guan, Chunxia 7 Guo, Yunxi 7 Klimsiak, Tomasz 7 Klingenberg, Christian 7 Liu, Tao 7 Majee, Ananta K. 7 Rohde, Christian 7 Rossi, Elena 7 Shen, Chun 7 Vallet, Guy 7 Wu, Yonghong 7 Yan, Haibo 7 Zhou, Shouming 6 Berres, Stefan 6 Csomós, Petra 6 Donadello, Carlotta 6 Duan, Jinqiao 6 Eymard, Robert 6 Feng, Zhaosheng 6 Flåtten, Tore 6 Frid, Hermano 6 Fu, Ying 6 Garavello, Mauro 6 Kacur, Jozef 6 Leach, Peter Gavin Lawrence 6 Li, Yachun 6 Mitrovic, Darko 6 Mou, Chenchen 6 Qiao, Zhijun 6 Qu, Changzheng 6 Shen, Wen 6 Storrøsten, Erlend Briseid 6 Sun, Meina 6 Świȩch, Andrzej 6 Wang, Guodong 6 Wu, Jianglun 5 Ainseba, Bedr’Eddine 5 Alibaud, Nathaël 5 Amadori, Debora 5 Barles, Guy 5 Chalons, Christophe 5 Cifani, Simone 5 del Teso, Félix 5 Di Francesco, Marco 5 dos Santos, Gelson C. 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