WIAS Preprint No. 3007, (2023)

Existence of similarity profiles for diffusion equations and systems


Authors

  • Mielke, Alexander
    ORCID: 0000-0002-4583-3888
  • Schindler, Stefanie
    ORCID: 0000-0002-4005-7314

2020 Mathematics Subject Classification

  • 35C06 35K40 35K57 35K65 80M30

Keywords

  • Self-similarity, similarity profiles, reaction-diffusion systems, constrained profile equation, monotone operators

DOI

10.20347/WIAS.PREPRINT.3007

Abstract

We study the existence of self-similar profiles for diffusion equations and reaction-diffusion systems on the real line, where different nontrivial limits are imposed at both sides of infinity. The theses profiles solve a coupled system of nonlinear ODEs that can be treated by monotone operator theory.

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