Existence of similarity profiles for diffusion equations and systems

2023/01/25 by Alexander Mielke, Mielke, Alexander, Schindler, Stefanie
Computer Science · Engineering · Mathematics · #35C06 #35K40 #35K57 #35K65 #80M30 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2301.10360

openalex publication_date 2023/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We study the existence of similarity profiles for diffusion equations and reaction diffusion systems on the real line, where the different nontrivial limits are imposed for x → -∞ and x → +∞. Theses similarity profiles solve a coupled system of nonlinear ODEs that can be treated by monotone operator theory.

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