World's Best Scientists 2026 revealed!

Overview

Grzegorz Karch is affiliated with the University of Wrocław in Poland and specializes in mathematics and computer science. Their research spans several subfields, including computational theory and mathematics, applied mathematics, modeling and simulation, computer networks and communications, and numerical analysis.

The scientist's work covers key topics such as advanced mathematical modeling in engineering, mathematical biology tumor growth, nonlinear dynamics and pattern formation, differential equations and numerical methods, mathematical and theoretical epidemiology and ecology models, Navier-Stokes equation solutions, as well as advanced mathematical physics problems.

Recent publications by Grzegorz Karch reflect these diverse interests. They include:

  • Instability of all regular stationary solutions to reaction-diffusion-ODE systems (2022, Journal of Differential Equations)
  • Stable discontinuous stationary solutions to reaction-diffusion-ODE systems (2023, Communications in Partial Differential Equations)
  • Stability of singular solutions to the Navier-Stokes system (2022, Journal of Differential Equations)
  • A Framework for Nonlocal, Nonlinear Initial Value Problems (2020, SIAM Journal on Mathematical Analysis)
  • Mathematical treatment of PDE model of chemotactic E. coli colonies (2021, Journal of Differential Equations)

Grzegorz Karch collaborates frequently with several researchers. Frequent coauthors include Szymon Cygan, Anna Marciniak-Czochra, Piotr Biler, Hiroshi Wakui, and Alexandre Boritchev.

Their publications are found in journals and venues such as arXiv, Journal of Differential Equations, Communications in Partial Differential Equations, SIAM Journal on Mathematical Analysis, and Journal of Evolution Equations. ArXiv hosts the largest number of their publications, followed by the Journal of Differential Equations.

Best Publications

  • Selfsimilar profiles in large time asymptotics of solutions to damped wave equations

    Grzegorz Karch

  • The 8π-problem for radially symmetric solutions of a chemotaxis model in the plane

    Piotr Biler;Grzegorz Karch;Philippe Laurençot;Tadeusz Nadzieja

  • Critical nonlinearity exponent and self-similar asymptotics for Lévy conservation laws

    Piotr Biler;Grzegorz Karch;Wojbor A Woyczyński

  • Smooth or singular solutions to the Navier-Stokes system ?

    Marco Cannone;Grzegorz Karch;Grzegorz Karch

  • Asymptotic Behaviour of Solutions to some Pseudoparabolic Equations

    Grzegorz Karch

  • Blowup of solutions to generalized Keller–Segel model

    Piotr Biler;Grzegorz Karch

  • The Nonlocal Porous Medium Equation: Barenblatt Profiles and Other Weak Solutions

    Piotr Biler;Cyril Imbert;Grzegorz Karch

  • Global regular and singular solutions for a model of gravitating particles

    Piotr Biler;Marco Cannone;Ignacio A. Guerra;Grzegorz Karch

  • Asymptotics for conservation laws involving Levy diffusion generators

    Piotr Biler;Grzegorz Karch;Wojbor A. Woyczyński

  • Asymptotics for multifractal conservation laws

    Piotr Biler;Grzegorz Karch;Wojbor A. Woyczynski

  • Barenblatt profiles for a nonlocal porous medium equation

    Piotr Biler;Cyril Imbert;Grzegorz Karch

  • The $8\pi$-problem for radially symmetric solutions of a chemotaxis model in a disc

    Piotr Cezary Biler;Grzegorz Karch;Philippe Laurençot;Tadeusz Nadzieja

  • Scaling in Nonlinear Parabolic Equations

    Grzegorz Karch

  • Nonlocal porous medium equation: Barenblatt profiles and other weak solutions

    Piotr Biler;Cyril Imbert;Grzegorz Karch

  • Nonlinear Diffusion of Dislocation Density and Self-Similar Solutions

    Piotr Biler;Grzegorz Karch;Régis Monneau

  • Asymptotic Properties of Entropy Solutions to Fractal Burgers Equation

    Nathael Alibaud;Cyril Imbert;Grzegorz Karch

  • Fractal Hamilton-Jacobi-KPZ equations

    Grzegorz Karch;Wojbor A. Woyczynski

  • Self-similar large time behavior of solutions to Korteweg-de Vries-Burgers equation

    Grzegorz Karch

  • Asymptotic profiles of solutions to viscous Hamilton-Jacobi equations

    Saïd Benachour;Grzegorz Karch;Philippe Laurençot

  • Barenblatt profiles for a nonlocal porous media equation

    Piotr Biler;Cyril Imbert;Grzegorz Karch

Frequent Co-Authors

Philippe Laurençot
Philippe Laurençot Toulouse Mathematics Institute
Cyril Imbert
Cyril Imbert École Normale Supérieure
Jean Dolbeault
Jean Dolbeault Paris Dauphine University
Masayasu Mimura
Masayasu Mimura Hiroshima University
Maria J. Esteban
Maria J. Esteban Paris Dauphine University

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