Kenneth Aksel Hvistendahl Karlsen

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Phone +47 22855948
Room 1009
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Visiting address Moltke Moes vei 35 Niels Henrik Abels hus 0851 Oslo
Postal address Postboks 1053 Blindern 0316 Oslo

Research interests

Nonlinear partial differential equations (PDEs) have their origin in the quest to describe nature by mathematics. However, several key questions have not been answered, or only been partly answered. Indeed, central issues in my research are: (1) Do the PDEs have a solution? (2) Given that the PDE has a solution, is it unique? (3) Is the solution stable with respect to changes in the input data? (4) If the equation has a unique and stable solution, how can one compute the solution by numerical algorithms? Variations of these questions for selected classes of PDEs and stochastic PDEs (SPDEs) constitute the main focus of my research, including the interplay between theoretical results (mathematical properties of the solution) and numerical computations (how to compute the solution). Most of the activity is basic mathematical research, but the PDE models are motivated by applications, including porous media flow (oil recovery), solid-liquid separation processes (sedimentation), traffic flow, water waves, finance, biology & medicine.


Editorial boards

SIAM Journal on Mathematical Analysis (2021–)

SIAM Journal on Numerical Analysis (2007–)

Journal of Hyperbolic Differential Equations (2004–)

Networks and Heterogeneous Media (2006– / EiC from 2017)

AIMS Book Series: Applied Mathematics (2011–)

Advances in Numerical Analysis (2008-2018)

Advances in Applied Mathematics and Mechanics (2009-2018)

Tags: Mathematics, Partial Differential Equations, China, Brazil, Russia, USA

Publications

  • Karlsen, Kenneth Aksel Hvistendahl & Holden, Helge (2022). Global well-posedness of the viscous Camassa–Holm equation with gradient noise. Discrete and Continuous Dynamical Systems. Series A. ISSN 1078-0947. doi: 10.3934/dcds.2022163.
  • Bendahmane, Mostafa & Karlsen, Kenneth Aksel Hvistendahl (2022). Martingale solutions of stochastic nonlocal cross-diffusion systems. Networks and Heterogeneous Media. ISSN 1556-1801. 17(5), p. 719–752. doi: 10.3934/nhm.2022024.
  • Frid, Hermano; Karlsen, Kenneth Aksel Hvistendahl & Marroquin, Daniel (2022). Homogenization of stochastic conservation laws with multiplicative noise. Journal of Functional Analysis. ISSN 0022-1236. 283(9), p. 1–63. doi: 10.1016/j.jfa.2022.109620.
  • Holden, Helge; Karlsen, Kenneth Aksel Hvistendahl & Pang, Ho Cheung (2022). Strong solutions of a stochastic differential equation with irregular random drift. Stochastic Processes and their Applications. ISSN 0304-4149. 150, p. 655–677. doi: 10.1016/j.spa.2022.05.006. Full text in Research Archive
  • Galimberti, Luca & Karlsen, Kenneth H. (2021). Renormalization of stochastic continuity equations on Riemannian manifolds. Stochastic Processes and their Applications. ISSN 0304-4149. 142, p. 195–244. doi: 10.1016/j.spa.2021.08.009. Full text in Research Archive
  • Holden, Helge; Karlsen, Kenneth Hvistendahl & Pang, Ho Cheung (2021). The Hunter-Saxton equation with noise. Journal of Differential Equations. ISSN 0022-0396. 270, p. 725–786. doi: 10.1016/j.jde.2020.07.031. Full text in Research Archive
  • Hoel, Håkon; Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik & Storrøsten, Erlend Briseid (2020). Numerical methods for conservation laws with rough flux. Stochastics and Partial Differential Equations: Analysis and Computations. ISSN 2194-0401. 8(1), p. 186–261. doi: 10.1007/s40072-019-00145-7. Full text in Research Archive
  • Galimberti, Luca & Karlsen, Kenneth Hvistendahl (2019). Well-posedness theory for stochastically forced conservation laws on Riemannian manifolds. Journal of Hyperbolic Differential Equations. ISSN 0219-8916. 16(3), p. 519–593. doi: 10.1142/S0219891619500188. Full text in Research Archive
  • Grandelius, Erik & Karlsen, Kenneth Hvistendahl (2019). The cardiac bidomain model and homogenization. Networks and Heterogeneous Media. ISSN 1556-1801. 14(1), p. 173–204. doi: 10.3934/nhm.2019009. Full text in Research Archive
  • Bendahmane, M. & Karlsen, Kenneth Hvistendahl (2019). Stochastically forced cardiac bidomain model. Stochastic Processes and their Applications. ISSN 0304-4149. 129(12), p. 5312–5363. doi: 10.1016/j.spa.2019.03.001. Full text in Research Archive
  • Coclite, Giuseppe Maria; di Ruvo, Lorenzo & Karlsen, Kenneth Hvistendahl (2018). The initial-boundary-value problem for an Ostrovsky-Hunter type equation, Non-linear Partial Differential Equations, Mathematical Physics, and Stochastic Analysis: The Helge Holden Anniversary Volume. European Mathematical Society (EMS) Publishing House. ISSN 978-3-03719-186-6. p. 97–109. doi: 10.4171/186-1/5.
  • Hoel, Håkon; Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik & Storrøsten, Erlend Briseid (2018). Path-dependent convex conservation laws. Journal of Differential Equations. ISSN 0022-0396. 265(6), p. 2708–2744. doi: 10.1016/j.jde.2018.04.045. Full text in Research Archive
  • Karlsen, Kenneth Hvistendahl & Towers, John D. (2017). Convergence of a Godunov scheme for conservation laws with a discontinuous flux lacking the crossing condition. Journal of Hyperbolic Differential Equations. ISSN 0219-8916. 14(4), p. 671–701. doi: 10.1142/S0219891617500229. Full text in Research Archive
  • Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik & Storrøsten, Erlend Briseid (2017). Practical Convergence Rates for Degenerate Parabolic Equations. In Gosse, Laurent & Natalini, Roberto (Ed.), Innovative Algorithms and Analysis. Springer. ISSN 978-3-319-49261-2. p. 243–263. Full text in Research Archive
  • Karlsen, Kenneth Hvistendahl & Storrøsten, Erlend Briseid (2017). Analysis of a splitting method for stochastic balance laws . IMA Journal of Numerical Analysis. ISSN 0272-4979. 38(1), p. 1–56. doi: 10.1093/imanum/drw075. Full text in Research Archive
  • Karlsen, Kenneth Hvistendahl & Towers, J. D. (2017). Convergence of Monotone Schemes for Conservation Laws with Zero-Flux Boundary Conditions. Advances in Applied Mathematics and Mechanics. ISSN 2070-0733. 9(3), p. 515–542. doi: 10.4208/aamm.2016.m-s1. Full text in Research Archive
  • Karlsen, Kenneth Hvistendahl & Storrøsten, Erlend Briseid (2017). On stochastic conservation laws and Malliavin calculus. Journal of Functional Analysis. ISSN 0022-1236. 272(2), p. 421–497. doi: 10.1016/j.jfa.2016.09.020. Full text in Research Archive
  • Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik & Storrøsten, Erlend Briseid (2016). On the convergence rate of finite difference methods for degenerate convection-diffusion equations in several space dimensions. Mathematical Modelling and Numerical Analysis. ISSN 0764-583X. 50(2), p. 499–539. doi: 10.1051/m2an/2015057.
  • Karlsen, Kenneth Hvistendahl & Ulusoy, Suleyman (2016). On a hyperbolic keller-segel system with degenerate nonlinear fractional diffusion. Networks and Heterogeneous Media. ISSN 1556-1801. 11(1), p. 181–201. doi: 10.3934/nhm.2016.11.181.
  • Biswas, Imran Habib; Karlsen, Kenneth Hvistendahl & Majee, Ananta K. (2015). Conservation laws driven by Lévy white noise. Journal of Hyperbolic Differential Equations. ISSN 0219-8916. 12(3), p. 581–654. doi: 10.1142/S0219891615500174.
  • Coclite, Giuseppe Maria & Karlsen, Kenneth Hvistendahl (2015). A note on the Camassa-Holm equation. Journal of Differential Equations. ISSN 0022-0396. 259(6), p. 2158–2166. doi: 10.1016/j.jde.2015.03.020.
  • Coclite, Giuseppe Maria & Karlsen, Kenneth Hvistendahl (2015). Periodic solutions of the Degasperis-Procesi equation: Well-posedness and asymptotics. Journal of Functional Analysis. ISSN 0022-1236. 268(5), p. 1053–1077. doi: 10.1016/j.jfa.2014.11.008.
  • Coclite, Giuseppe Maria; di Ruvo, L & Karlsen, Kenneth Hvistendahl (2014). Some wellposedness results for the Ostrovsky-Hunter equation. Springer Proceedings in Mathematics & Statistics. ISSN 2194-1017. 49, p. 143–159. doi: 10.1007/978-3-642-39007-4_7.
  • Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik & Storrøsten, Erlend Briseid (2014). L1 error estimates for difference approximations of degenerate convection-diffusion equations. Mathematics of Computation. ISSN 0025-5718. 83(290), p. 2717–2762. doi: 10.1090/S0025-5718-2014-02818-4.
  • Kissling, Frederike & Karlsen, Kenneth Hvistendahl (2014). On the singular limit of a two-phase flow equation with heterogeneities and dynamic capillary pressure. Zeitschrift für angewandte Mathematik und Mechanik. ISSN 0044-2267. 94(7-8), p. 678–689. doi: 10.1002/zamm.201200141.
  • Bendahmane, Mostafa; Karlsen, Kenneth Hvistendahl & Saad, Mazen (2013). Nonlinear anisotropic elliptic and parabolic equations with variable exponents and L/1 data. Communications on Pure and Applied Analysis. ISSN 1534-0392. 12(3), p. 1201–1220. doi: 10.3934/cpaa.2013.12.1201.
  • Holden, Helge; Karlsen, Kenneth Hvistendahl & Karper, Trygve Klovning (2013). Operator splitting for two-dimensional incompressible fluid equations. Mathematics of Computation. ISSN 0025-5718. 82(282), p. 719–748. doi: 10.1090/s0025-5718-2012-02626-3.
  • Holden, Helge; Karlsen, Kenneth Hvistendahl & Karper, Trygve Klovning (2013). OPERATOR SPLITTING FOR WELL-POSED ACTIVE SCALAR EQUATIONS. SIAM Journal on Mathematical Analysis. ISSN 0036-1410. 45(1), p. 152–180. doi: 10.1137/120864337.
  • Chen, Gui-Qiang; Ding, Qian & Karlsen, Kenneth Hvistendahl (2012). On Nonlinear Stochastic Balance Laws. Archive for Rational Mechanics and Analysis. ISSN 0003-9527. 204(3), p. 707–743. doi: 10.1007/s00205-011-0489-9.
  • Bendahmane, Mostafa & Karlsen, Kenneth Hvistendahl (2012). A note on entropy solutions for degenerate parabolic equations with L^1\cap L^p data. International Journal of Dynamical Systems and Differential Equations. ISSN 1752-3583. 4, p. 78–92. doi: 10.1504/ijdsde.2012.045996.
  • Karlsen, Kenneth Hvistendahl & Karper, Trygve Klovning (2012). A convergent mixed method for the Stokes approximation of viscous compressible flow. IMA Journal of Numerical Analysis. ISSN 0272-4979. 32(3), p. 725–764. doi: 10.1093/imanum/drq048.
  • Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik & Koley, Ujjwal (2012). An error estimate for the finite difference approximation to degenerate convection-diffusion equations. Numerische Mathematik. ISSN 0029-599X. 121(2), p. 367–395. doi: 10.1007/s00211-011-0433-9.
  • Coclite, Giuseppe Maria; Karlsen, Kenneth Hvistendahl; Mishra, Siddhartha & Risebro, Nils Henrik (2012). A HYPERBOLIC-ELLIPTIC MODEL OF TWO-PHASE FLOW IN POROUS MEDIA EXISTENCE OF ENTROPY SOLUTIONS. International Journal of Numerical Analysis & Modeling. ISSN 1705-5105. 9(3), p. 562–583.
  • Coclite, Giuseppe Maria & Karlsen, Kenneth Hvistendahl (2012). On an initial-boundary value problem for the hyperelastic rod wave equation. Advances in Differential Equations. ISSN 1079-9389. 17(1-2), p. 37–74.
  • Evje, Steinar & Karlsen, Kenneth Hvistendahl (2012). ANALYSIS OF A COMPRESSIBLE GAS-LIQUID MODEL MOTIVATED BY OIL WELL CONTROL OPERATIONS. Acta Mathematica Scientia. ISSN 0252-9602. 32(1), p. 295–314.
  • Karlsen, Kenneth Hvistendahl & Ulusoy, Suleyman (2011). Stability of entropy solutions for Lévy mixed hyperbolic-parabolic equations. Electronic Journal of Differential Equations. ISSN 1550-6150. 116, p. 1–23.
  • Cifani, Simone; Jakobsen, Espen Robstad & Karlsen, Kenneth Hvistendahl (2011). The discontinuous Galerkin method for fractional degenerate convection-diffusion equations. BIT Numerical Mathematics. ISSN 0006-3835. 51(4), p. 809–844. doi: 10.1007/s10543-011-0327-3.
  • Frid, Hermano; Holden, Helge & Karlsen, Kenneth Hvistendahl (2011). L-infinity SOLUTIONS FOR A MODEL OF NONISOTHERMAL POLYTROPIC GAS FLOW. SIAM Journal on Mathematical Analysis. ISSN 0036-1410. 43(5), p. 2253–2274. doi: 10.1137/110824218.
  • Andreianov, Boris; Bendahmane, Mostafa; Karlsen, Kenneth Hvistendahl & Pierre, Charles (2011). CONVERGENCE OF DISCRETE DUALITY FINITE VOLUME SCHEMES FOR THE CARDIAC BIDOMAIN MODEL. Networks and Heterogeneous Media. ISSN 1556-1801. 6(2), p. 195–240. doi: 10.3934/nhm.2011.6.195.
  • Cifani, Simone; Jakobsen, Espen Robstad & Karlsen, Kenneth Hvistendahl (2011). The discontinuous Galerkin method for fractal conservation laws. IMA Journal of Numerical Analysis. ISSN 0272-4979. 31(3), p. 1090–1122. doi: 10.1093/imanum/drq006.
  • Karlsen, Kenneth Hvistendahl & Karper, Trygve Klovning (2011). CONVERGENCE OF A MIXED METHOD FOR A SEMI-STATIONARY COMPRESSIBLE STOKES SYSTEM. Mathematics of Computation. ISSN 0025-5718. 80(275), p. 1459–1498. doi: 10.1090/s0025-5718-2010-02446-9.
  • Andreianov, Boris; Karlsen, Kenneth Hvistendahl & Risebro, Nils Henrik (2011). A Theory of L (1)-Dissipative Solvers for Scalar Conservation Laws with Discontinuous Flux. Archive for Rational Mechanics and Analysis. ISSN 0003-9527. 201(1), p. 27–86. doi: 10.1007/s00205-010-0389-4.
  • Betancourt, F.; Bürger, R. & Karlsen, Kenneth Hvistendahl (2011). A STRONGLY DEGENERATE PARABOLIC AGGREGATION EQUATION. Communications in Mathematical Sciences. ISSN 1539-6746. 9(3), p. 711–742. doi: 10.4310/cms.2011.v9.n3.a4.
  • Holden, Helge; Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik & Tao, T (2011). OPERATOR SPLITTING FOR THE KdV EQUATION. Mathematics of Computation. ISSN 0025-5718. 80(274), p. 821–846. doi: 10.1090/S0025-5718-2010-02402-0.
  • Betancourt, F.; Bürger, R.; Karlsen, Kenneth Hvistendahl & Tory, E.M. (2011). On nonlocal conservation laws modelling sedimentation. Nonlinearity. ISSN 0951-7715. 24(3), p. 855–885. doi: 10.1088/0951-7715/24/3/008.
  • Karlsen, Kenneth Hvistendahl; Petitta, Francesco & Ulusoy, Suleyman (2011). A duality approach to the fractional Laplacian with measure data. Publicacions matemàtiques. ISSN 0214-1493. 55(1), p. 151–161.
  • Guan, C.; Karlsen, Kenneth Hvistendahl & Yin, Z. (2010). Well-posedness and blow-up phenomena for a modified two-component Camassa-Holm equation. In Holden, Helge & Karlsen, Kenneth Hvistendahl (Ed.), Nonlinear partial differential equations and hyperbolic wave phenomena. American Mathematical Society (AMS). ISSN 978-0-8218-4976-7. p. 199–220.
  • Bürger, Raimund; Karlsen, Kenneth Hvistendahl; Torres, Héctor & Towers, John D. (2010). Second-order schemes for conservation laws with discontinuous flux modelling clarifier-thickener units. Numerische Mathematik. ISSN 0029-599X. 116(4), p. 579–617. doi: 10.1007/s00211-010-0325-4.
  • Karlsen, Kenneth Hvistendahl & Karper, Trygve Klovning (2010). A CONVERGENT NONCONFORMING FINITE ELEMENT METHOD FOR COMPRESSIBLE STOKES FLOW. SIAM Journal on Numerical Analysis. ISSN 0036-1429. 48(5), p. 1846–1876. doi: 10.1137/09076310X.
  • Biswas, Imran Habib; Jakobsen, Espen Robstad & Karlsen, Kenneth Hvistendahl (2010). DIFFERENCE-QUADRATURE SCHEMES FOR NONLINEAR DEGENERATE PARABOLIC INTEGRO-PDE. SIAM Journal on Numerical Analysis. ISSN 0036-1429. 48(3), p. 1110–1135. doi: 10.1137/090761501.
  • Andreianov, Boris; Bendahmane, Mostafa & Karlsen, Kenneth Hvistendahl (2010). DISCRETE DUALITY FINITE VOLUME SCHEMES FOR DOUBLY NONLINEAR DEGENERATE HYPERBOLIC-PARABOLIC EQUATIONS. Journal of Hyperbolic Differential Equations. ISSN 0219-8916. 7(1), p. 1–67. doi: 10.1142/S0219891610002062.
  • Bürger, Raimond; Karlsen, Kenneth Hvistendahl & Towers, John D. (2010). ON SOME DIFFERENCE SCHEMES AND ENTROPY CONDITIONS FOR A CLASS OF MULTI-SPECIES KINEMATIC FLOW MODELS WITH DISCONTINUOUS FLUX. Networks and Heterogeneous Media. ISSN 1556-1801. 5(3), p. 461–485. doi: 10.3934/nhm.2010.5.461.
  • Andreianov, Boris; Karlsen, Kenneth Hvistendahl & Risebro, Nils Henrik (2010). ON VANISHING VISCOSITY APPROXIMATION OF CONSERVATION LAWS WITH DISCONTINUOUS FLUX. Networks and Heterogeneous Media. ISSN 1556-1801. 5(3), p. 617–633. doi: 10.3934/nhm.2010.5.617.
  • Biswas, IH; Jakobsen, Espen Robstad & Karlsen, KH (2010). Viscosity Solutions for a System of Integro-PDEs and Connections to Optimal Switching and Control of Jump-Diffusion Processes. Applied Mathematics and Optimization. ISSN 0095-4616. 62(1), p. 47–80. doi: 10.1007/s00245-009-9095-8.
  • Evje, Steinar & Karlsen, Kenneth Hvistendahl (2009). Global Weak Solutions for a Viscous Liquid-Gas Model with Singular Pressure Law. Communications on Pure and Applied Analysis. ISSN 1534-0392. 8(6), p. 1867–1894.
  • Nilssen, Trygve Kastberg; Karlsen, Kenneth Hvistendahl; Mannseth, T. & Tai, XC (2009). Identification of diffusion parameters in a nonlinear convection-diffusion equation using the augmented Lagrangian method. Computational Geosciences. ISSN 1420-0597. 13(3), p. 317–329.
  • Burger, R; Karlsen, Kenneth Hvistendahl & Towers, J. D. (2009). A conservation law with discontinuous flux modelling traffic flow with abruptly changing road surface conditions. In Tadmor, Eitan; Liu, Jian-Guo & Tzavaras, Athanasios E. (Ed.), Hyperbolic Problems: Theory, Numerics and Applications. American Mathematical Society (AMS). ISSN 978-0-8218-4728-2. p. 455–464.
  • Karlsen, Kenneth Hvistendahl & Karper, Trygve Klovning (2009). Convergent finite element methods for compressible barotropic Stokes systems. In Tadmor, Eitan; Liu, Jian-Guo & Tzavaras, Athanasios E. (Ed.), Hyperbolic Problems: Theory, Numerics and Applications. American Mathematical Society (AMS). ISSN 978-0-8218-4728-2. p. 705–714.
  • Nilssen, Trygve Kastberg; Karlsen, Kenneth Hvistendahl ; Mannseth, Trond & Tai, Xue-Cheng (2009). Identification of diffusion parameters in a nonlinear convection-diffusion equation using the augmented Lagrangian method. Computational Geosciences. ISSN 1420-0597. 13(3), p. 317–329. doi: 10.1007/s10596-008-9120-z.
  • Karlsen, Kenneth Hvistendahl; Mishra, Siddhartha & Risebro, Nils Henrik (2009). WELL-BALANCED SCHEMES FOR CONSERVATION LAWS WITH SOURCE TERMS BASED ON A LOCAL DISCONTINUOUS FLUX FORMULATION. Mathematics of Computation. ISSN 0025-5718. 78(265), p. 55–78.
  • Karlsen, Kenneth Hvistendahl; Mishra, Siddhartha & Risebro, Nils Henrik (2009). Convergence of finite volume schemes for triangular systems of conservation laws. Numerische Mathematik. ISSN 0029-599X. 111(4), p. 559–589. doi: 10.1007/s00211-008-0199-x.
  • Holden, Helge; Coclite, Giuseppe Maria & Karlsen, Kenneth Hvistendahl (2009). Well-posedness of higher-order Camassa-Holm equations. Journal of Differential Equations. ISSN 0022-0396. 246(3), p. 929–963. doi: 10.1016/j.jde.2008.04.014.
  • Holden, Helge; Karlsen, Kenneth Hvistendahl & Mitrovic, Darko (2009). Zero diffusion-dispersion-smoothing limits for a scalar conservation law with discontinuous flux function. International Journal of Differential Equations. ISSN 1687-9643. 2009. doi: 10.1155/2009/279818.
  • Holden, Helge; Karlsen, KH & Risebro, N.H. (2009). A convergent finite-difference method for a nonlinear variational wave equation. IMA Journal of Numerical Analysis. ISSN 0272-4979. 29(3), p. 539–572. doi: 10.1093/imanum/drn026.
  • Coclite, GM; Karlsen, Kenneth Hvistendahl & Kwon, YS (2009). Initial-boundary value problems for conservation laws with source terms and the Degasperis-Procesi equation. Journal of Functional Analysis. ISSN 0022-1236. 257(12), p. 3823–3857. doi: 10.1016/j.jfa.2009.09.022.
  • Holden, Helge; Karlsen, Kenneth Hvistendahl; Mitrovic, Darko & Panov, Evgueni Yu (2009). Strong compactness of approximated solutions to degenerate elliptic-hyperbolic equations with discontinuous flux function. Acta Mathematica Scientia. ISSN 0252-9602. 29(6), p. 1573–1612.
  • Evje, Steinar & Karlsen, Kenneth Hvistendahl (2009). GLOBAL WEAK SOLUTIONS FOR A VISCOUS LIQUID-GAS MODEL WITH SINGULAR PRESSURE LAW. Communications on Pure and Applied Analysis. ISSN 1534-0392. 8(6), p. 1867–1894. doi: 10.3934/cpaa.2009.8.1867.
  • Andreianov, Boris; Bendahmane, Mostafa; Karlsen, Kenneth Hvistendahl & Ouaro, Stanislas (2009). Well-posedness results for triply nonlinear degenerate parabolic equations. Journal of Differential Equations. ISSN 0022-0396. 247(1), p. 277–302. doi: 10.1016/j.jde.2009.03.001.
  • Risebro, Nils Henrik; Karlsen, Kenneth Hvistendahl & Coclite, Giuseppe Maria (2009). Convergence of vanishing viscos- ity approximations of 2x2 triangular systems of multi-dimensional conservation laws. Bollettino dell'Unione Matematica Italiana, Sezione B.. ISSN 0392-4041. 9(2), p. 275–284.
  • Karlsen, Kenneth Hvistendahl; Mishra, Siddhartha & Risebro, Nils Henrik (2009). Semi-Godunov schemes for multiphase flows in porous media. Applied Numerical Mathematics. ISSN 0168-9274. 59(9), p. 2322–2336. doi: 10.1016/j.apnum.2008.12.019.
  • Karlsen, Kenneth Hvistendahl; Fuchs, Franz Georg; Mishra, Siddhartha & Risebro, Nils Henrik (2009). Stable upwind schemes for the magnetic induction equation. Mathematical Modelling and Numerical Analysis. ISSN 0764-583X. 43(5), p. 825–852. doi: 10.1051/m2an/2009006.
  • Bendahmane, Mostafa & Karlsen, Kenneth Hvistendahl (2009). Convergence of a finite volume scheme for the bidomain model of cardiac tissue. Applied Numerical Mathematics. ISSN 0168-9274. 59(9), p. 2266–2284. doi: 10.1016/j.apnum.2008.12.016.
  • Burger, Raimund; Karlsen, Kenneth Hvistendahl & Towers, John D. (2009). An Engquist-Osher-type scheme for conservation laws with discontinuous flux adapted to flux connections. SIAM Journal on Numerical Analysis. ISSN 0036-1429. 47(3), p. 1684–1712.
  • Holden, Helge; Karlsen, Kenneth Hvistendahl & Mitrovic, D (2009). Zero diffusion-dispersion-smoothing limits for scalar conservation law with discontinuous flux function. International Journal of Differential Equations. ISSN 1687-9643.
  • Wallin, Olli & Karlsen, Kenneth Hvistendahl (2009). A semilinear equation for the American option in a general jump market. Interfaces and free boundaries (Print). ISSN 1463-9963. 11, p. 475–501.
  • Karlsen, Kenneth Hvistendahl & Wallin, Olli (2009). A semilinear equation for the American option in a general jump market. Interfaces and free boundaries (Print). ISSN 1463-9963. 11(4), p. 475–501.
  • Holden, Helge; Karlsen, Kenneth Hvistendahl & Coclite, Giuseppe Maria (2008). Global weak solutions for a shallow water equation. In Benzoni-Gavage, Sylvie & Serre, Denis (Ed.), Hyperbolic Problems: Theory, Numerics, Applications. Springer. ISSN 9783540757115. p. 389–396.
  • Karlsen, Kenneth Hvistendahl; Coclite, Giuseppe Maria & Holden, Helge (2008). Global weak solutions for a shallow water equation. In Benzoni-Gavage, Sylvie & Serre, Denis (Ed.), Hyperbolic Problems: Theory, Numerics, Applications. Proceedings of the Eleventh International Conference on Hyperbolic Problems held in Ecole Normale Supérieure, Lyon, July 17-21, 2006. Springer. ISSN 978-3-540-75711-5. p. 389–396.
  • Karlsen, Kenneth Hvistendahl & Evje, Steinar (2008). A hyperbolic-elliptic model for coupled well-porous media flow. In Benzoni-Gavage, Sylvie & Serre, Denis (Ed.), Hyperbolic Problems: Theory, Numerics, Applications. Proceedings of the Eleventh International Conference on Hyperbolic Problems held in Ecole Normale Supérieure, Lyon, July 17-21, 2006. Springer. ISSN 978-3-540-75711-5. p. 493–501.
  • Biswas, Imran Habib; Jakobsen, Espen Robstad & Karlsen, Kenneth h. (2008). Error estimates for a class of finite difference-quadrature schemes for fully nonlinear degenerate parabolic integro-PDEs. Journal of Hyperbolic Differential Equations. ISSN 0219-8916. 5.
  • Burger, R; Garcia, A; Karlsen, Kenneth Hvistendahl & Towers, JD (2008). A family of numerical schemes for kinematic flows with discontinuous flux. Journal of Engineering Mathematics. ISSN 0022-0833. 60, p. 387–425. doi: 10.1007/s10665-007-9148-4.
  • Karlsen, Kenneth Hvistendahl; Mishra, Siddhartha & Risebro, Nils Henrik (2008). A large-time-stepping scheme for balance equations. Journal of Engineering Mathematics. ISSN 0022-0833. 60, p. 351–363. doi: 10.1007/s10665-007-9164-4.
  • Coclite, GM; Karlsen, Kenneth Hvistendahl & Risebro, Nils Henrik (2008). Numerical schemes for computing discontinuous solutions of the Degasperis-Procesi equation. IMA Journal of Numerical Analysis. ISSN 0272-4979. 28. doi: 10.1093/imanum/drm003.
  • Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik & Coclite, Giuseppe Maria (2008). A convergent finite difference scheme for the Camassa-Holm equation with general H^1 initial data. SIAM Journal on Numerical Analysis. ISSN 0036-1429. 46, p. 1554–1579.
  • Risebro, Nils Henrik; Karlsen, Kenneth Hvistendahl & Coclite, Giuseppe Maria (2008). An explicit finite difference scheme for the Camassa-Holm equation. Advances in Difference Equations. ISSN 1687-1839. 13(7-8), p. 681–732.
  • Risebro, Nils Henrik; Karlsen, Kenneth Hvistendahl & Holden, Helge (2008). A convergent finite difference method for a variational wave equation. IMA Journal of Numerical Analysis. ISSN 0272-4979. p. 1–34. doi: 10.1093/imanum/drn026.
  • Biswas, Imran Habib; Jakobsen, Espen Robstad; La Chioma, C & Karlsen, Kenneth h. (2008). Error estimates for approximate solutions to Bellman equations associated with controlled jump-diffusions. Numerische Mathematik. ISSN 0029-599X. 110, p. 221–255. doi: 10.1007/s00211-008-0160-z.
  • Evje, S & Karlsen, Kenneth Hvistendahl (2008). Global existence of weak solutions for a viscous two-phase model. Journal of Differential Equations. ISSN 0022-0396. 245(9), p. 2660–2703. doi: 10.1016/j.jde.2007.10.032.
  • Burger, R; Garcia, A; Karlsen, Kenneth Hvistendahl & Towers, JD (2008). A kinematic model of continuous separation and classification of polydisperse suspensions. Computers and Chemical Engineering. ISSN 0098-1354. 32, p. 1173–1194. doi: 10.1016/j.compchemeng.2007.04.019.
  • Bürger, Raimond & Karlsen, Kenneth Hvistendahl (2008). Conservation laws with discontinuous flux: a short introduction. Journal of Engineering Mathematics. ISSN 0022-0833. 60. doi: 10.1007/s10665-008-9213-7.
  • Karlsen, Kenneth Hvistendahl; Mishra, Siddhartha & Risebro, Nils Henrik (2008). Semi-Godunov schemes for general triangular systems of conservation laws. Journal of Engineering Mathematics. ISSN 0022-0833. 60. doi: 10.1007/s10665-007-9163-5.
  • Burger, R; Garcia, A; Karlsen, Kenneth Hvistendahl & Towers, JD (2008). Difference schemes, entropy solutions, and speedup impulse for an inhomogeneous kinematic traffic flow model. Networks and Heterogeneous Media. ISSN 1556-1801. 3.
  • Holden, Helge; Karlsen, Kenneth Hvistendahl & Risebro, Nils Henrik (2007). Convergent difference schemes for the Hunter-Saxton equation. Mathematics of Computation. ISSN 0025-5718. 76, p. 699–744.

View all works in Cristin

View all works in Cristin

  • Coclite, Giuseppe Maria; di Ruvo, Lorenzo & Karlsen, Kenneth Hvistendahl (2018). The initial-boundary-value problem for an Ostrovsky- Hunter type equation, Non-linear Partial Differential Equations, Mathematical Physics, and Stochastic Analysis: The Helge Holden Anniversary Volume. European Mathematical Society (EMS) Publishing House. ISSN 978-3-03719-186-6. p. 97–109.
  • Berre, Inga; Dahle, Helge K.; Karlsen, Kenneth Hvistendahl; Nordbotten, Jan Martin; Tai, Xue-Cheng & Winther, Ragnar (2012). Magne Espedal Memorial Issue. International Journal of Numerical Analysis & Modeling. ISSN 1705-5105. 9(3), p. I–II.
  • Rabenorolahy, David; Kalisch, Henrik & Karlsen, Kenneth Hvistendahl (2008). Relaxation schemes for degenerate parabolic convection diffusion equations with a discontinuous coefficient. Universitetet i Bergen.

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Published Nov. 30, 2010 11:20 PM - Last modified Aug. 23, 2022 2:10 PM

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