Distributional solutions of nonlinear diffusion equations with a moving Dirac source term
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.
Copyright (c) 2023 Marek Fila, Petra Macková, Jin Takahashi, Eiji Yanagida
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