D-Index & Metrics Best Publications
Mathematics
Norway
2022

D-Index & Metrics

Discipline name D-index D-index (Discipline H-index) only includes papers and citation values for an examined discipline in contrast to General H-index which accounts for publications across all disciplines. Citations Publications World Ranking National Ranking
Mathematics D-index 55 Citations 7,895 188 World Ranking 385 National Ranking 2

Research.com Recognitions

Awards & Achievements

2022 - Research.com Mathematics in Norway Leader Award

Member of the Norwegian Academy of Science and Letters Mathematics

Overview

What is he best known for?

The fields of study he is best known for:

  • Mathematical analysis
  • Partial differential equation
  • Geometry

Mathematical analysis, Uniqueness, Nonlinear system, Conservation law and Weak solution are his primary areas of study. His study on Mathematical analysis is mostly dedicated to connecting different topics, such as Rate of convergence. Kenneth H. Karlsen combines subjects such as Anisotropic diffusion, Compressibility, Polytropic process, Differential equation and Lipschitz continuity with his study of Uniqueness.

The Nonlinear system study combines topics in areas such as Law, Continuous-time stochastic process and Equicontinuity. Kenneth H. Karlsen interconnects Numerical analysis, Uniqueness theorem for Poisson's equation, Compact space and Piecewise in the investigation of issues within Conservation law. The various areas that Kenneth H. Karlsen examines in his Weak solution study include Semigroup, Burgers' equation, Convection and Camassa–Holm equation.

His most cited work include:

  • On the well-posedness of the Degasperis-Procesi equation (200 citations)
  • L¹ STABILITY FOR ENTROPY SOLUTIONS OF NONLINEAR DEGENERATE PARABOLIC CONVECTION-DIFFUSION EQUATIONS WITH DISCONTINUOUS COEFFICIENTS (135 citations)
  • Global weak solutions to a generalized hyperelastic-rod wave equation (133 citations)

What are the main themes of his work throughout his whole career to date?

His primary areas of investigation include Mathematical analysis, Conservation law, Nonlinear system, Uniqueness and Numerical analysis. His work in Weak solution, Initial value problem, Parabolic partial differential equation, Convection–diffusion equation and Finite difference method are all subfields of Mathematical analysis research. His Finite difference method research incorporates themes from Upwind scheme and Finite difference.

As a member of one scientific family, Kenneth H. Karlsen mostly works in the field of Conservation law, focusing on Applied mathematics and, on occasion, Monotone polygon. His biological study deals with issues like Viscosity solution, which deal with fields such as Bellman equation. His work focuses on many connections between Uniqueness and other disciplines, such as Compact space, that overlap with his field of interest in Finite volume method.

He most often published in these fields:

  • Mathematical analysis (67.76%)
  • Conservation law (32.65%)
  • Nonlinear system (31.84%)

What were the highlights of his more recent work (between 2013-2021)?

  • Conservation law (32.65%)
  • Applied mathematics (17.96%)
  • Mathematical analysis (67.76%)

In recent papers he was focusing on the following fields of study:

Kenneth H. Karlsen spends much of his time researching Conservation law, Applied mathematics, Mathematical analysis, Rate of convergence and Uniqueness. His studies deal with areas such as Differentiable function, Numerical analysis, Scalar and Regular polygon as well as Conservation law. He has researched Applied mathematics in several fields, including Boundary value problem and Compact space.

His Mathematical analysis study combines topics from a wide range of disciplines, such as Flow and Dispersion. Within one scientific family, he focuses on topics pertaining to Kinetic energy under Rate of convergence, and may sometimes address concerns connected to Finite volume method. His Finite difference method study also includes

  • Convection–diffusion equation which intersects with area such as Space dimension,
  • Space which intersects with area such as Parabolic partial differential equation and Dimension.

Between 2013 and 2021, his most popular works were:

  • Some Wellposedness Results for the Ostrovsky–Hunter Equation (25 citations)
  • On stochastic conservation laws and Malliavin calculus (20 citations)
  • Conservation laws driven by Lévy white noise (19 citations)

In his most recent research, the most cited papers focused on:

  • Mathematical analysis
  • Partial differential equation
  • Geometry

His main research concerns Conservation law, Mathematical analysis, Applied mathematics, Uniqueness and Entropy. His Conservation law research integrates issues from Rough path, Piecewise linear function, Scalar and Regular polygon. Kenneth H. Karlsen regularly links together related areas like Nonlinear evolution in his Mathematical analysis studies.

His Applied mathematics research includes elements of Differentiable function, Compact space and Camassa–Holm equation. His Uniqueness study integrates concerns from other disciplines, such as Initial value problem, Kondratiev wave, Boundary value problem and Godunov's scheme. His work deals with themes such as Finite difference, Monotone polygon, Kinetic energy and Nonlinear system, which intersect with Finite difference method.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Best Publications

On the well-posedness of the Degasperis-Procesi equation

Giuseppe M. Coclite;Kenneth H. Karlsen.
Journal of Functional Analysis (2006)

229 Citations

Splitting methods for partial differential equations with rough solutions : analysis and MATLAB programs

Helge Holden;Kenneth Hvistendahl Karlsen;Knut-Andreas Lie;Nils Henrik Risebro.
(2010)

214 Citations

L¹ STABILITY FOR ENTROPY SOLUTIONS OF NONLINEAR DEGENERATE PARABOLIC CONVECTION-DIFFUSION EQUATIONS WITH DISCONTINUOUS COEFFICIENTS

Kenneth H. Karlsen;Nils Henrik Risebro;John D. Towers.
(2003)

207 Citations

Strongly Degenerate Parabolic-Hyperbolic Systems Modeling Polydisperse Sedimentation with Compression

Elmer M. Tory;Kenneth H. Karlsen;Raimund Bürger;Stefan Berres.
Siam Journal on Applied Mathematics (2003)

198 Citations

A Theory of L 1 -Dissipative Solvers for Scalar Conservation Laws with Discontinuous Flux

Boris Andreianov;Kenneth Hvistendahl Karlsen;Nils Henrik Risebro.
Archive for Rational Mechanics and Analysis (2011)

180 Citations

On the uniqueness and stability of entropy solutions of nonlinear degenerate parabolic equations with rough coefficients

Kenneth Hvistendahl Karlsen;Nils Henrik Risebro.
Discrete and Continuous Dynamical Systems (2003)

173 Citations

Global weak solutions to a generalized hyperelastic-rod wave equation

Giuseppe Maria Coclite;Helge Holden;Kenneth H. Karlsen.
Siam Journal on Mathematical Analysis (2005)

154 Citations

CONVERGENCE OF THE LAX-FRIEDRICHS SCHEME AND STABILITY FOR CONSERVATION LAWS WITH A DISCONTINUOUS SPACE-TIME DEPENDENT FLUX

Kenneth H. Karlsen;John D. Towers.
Chinese Annals of Mathematics (2004)

141 Citations

Upwind difference approximations for degenerate parabolic convection–diffusion equations with a discontinuous coefficient

K. H. Karlsen;N. H. Risebro;J. D. Towers.
Ima Journal of Numerical Analysis (2002)

140 Citations

Well-posedness in BV t and convergence of a difference scheme for continuous sedimentation in ideal clarifier-thickener units

R. Bürger;K. H. Karlsen;N. H Risebro;J. D. Towers.
Numerische Mathematik (2004)

137 Citations

If you think any of the details on this page are incorrect, let us know.

Contact us

Best Scientists Citing Kenneth H. Karlsen

Raimund Bürger

Raimund Bürger

University of Concepción

Publications: 88

Helge Holden

Helge Holden

Norwegian University of Science and Technology

Publications: 41

Nils Henrik Risebro

Nils Henrik Risebro

University of Oslo

Publications: 37

Yue Liu

Yue Liu

The University of Texas at Arlington

Publications: 18

Gui-Qiang Chen

Gui-Qiang Chen

University of Oxford

Publications: 16

Rinaldo M. Colombo

Rinaldo M. Colombo

University of Brescia

Publications: 13

Panagiotis E. Souganidis

Panagiotis E. Souganidis

University of Chicago

Publications: 12

Thierry Gallouët

Thierry Gallouët

Aix-Marseille University

Publications: 11

Knut-Andreas Lie

Knut-Andreas Lie

SINTEF

Publications: 11

Guy Barles

Guy Barles

François Rabelais University

Publications: 11

Ingmar Nopens

Ingmar Nopens

Ghent University

Publications: 10

Yonghong Wu

Yonghong Wu

Curtin University

Publications: 10

Sze Chun Wong

Sze Chun Wong

University of Hong Kong

Publications: 9

Raphaèle Herbin

Raphaèle Herbin

Aix-Marseille University

Publications: 9

Robert Eymard

Robert Eymard

University of Paris-Est

Publications: 9

Benoît Perthame

Benoît Perthame

Sorbonne University

Publications: 8

Something went wrong. Please try again later.