Distributional solutions of nonlinear diffusion equations with a moving Dirac source term

Authors

  • Marek Fila Department of Applied Mathematics and Statistics, Comenius University, Bratislava, Slovakia
  • Petra Macková* Department of Applied Mathematics and Statistics, Comenius University, Bratislava, Slovakia
  • Jin Takahashi Department of Mathematical and Computing Science, Tokyo Institute of Technology, Tokyo, Japan
  • Eiji Yanagida Department of Mathematics, Tokyo Institute of Technology, Tokyo, Japan

Abstract

We focus on the study of singular solutions of nonlinear diffusion equations, specifically the fast diffusion and porous medium equations. Building on work on the existence of asymptotically radially symmetric solutions by Fila, Takahashi, and Yanagida, we focus on their uniqueness and the equation they satisfy in the sense of distributions. This equation involves a moving Dirac source term, which is also found in parabolic systems used in various biological applications.

Marek Fila, a supervisor, friend, and co-author of this paper, passed away in April 2023. In his memory, the second author has decided to publish the research, as this work with his valuable impact was finished before his passing.

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Published

2023-05-17

Issue

BIOMATH 2023

Section

Conference Contributions

License

Copyright (c) 2023 Marek Fila, Petra Macková, Jin Takahashi, Eiji Yanagida

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.