Existence of similarity profiles for diffusion equations and systems

TL;DR

This paper investigates the existence of similarity profiles for diffusion equations and systems with different asymptotic limits at infinity, using monotone operator theory to solve the resulting nonlinear ODE systems.

Contribution

It establishes the existence of such profiles for coupled nonlinear ODE systems arising from diffusion equations with asymmetric boundary conditions.

Findings

Existence of similarity profiles for specific diffusion systems.

Application of monotone operator theory to nonlinear ODEs.

Profiles exhibit different limits at ± infinity.

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 \to -\infty$ and $x \to +\infty$. Theses similarity profiles solve a coupled system of nonlinear ODEs that can be treated by monotone operator theory.