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
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.
Appeared in
- NoDEA Nonlinear Differential Equations Appl., 32 (2025), pp. 14/1--14/33 (published online on 11.12.2024), DOI 10.1007/s00030-024-01009-3 .
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