Front formation in the reaction-diffusion problem with nonlinear diffusion

A. R. Makhmudov, A. O. Orlov, V.T. Volkov

Lomonosov Moscow State University

Abstract: The process of the formation of a front-type solution in the reaction-diffusion equation in the case of spatially inhomogeneous nonlinear diffusion is considered. Sufficient conditions are formulated to ensure the formation of a sharp inner transition layer (front) in a neighborhood of a certain point, and estimates of the duration of the transition process are obtained.

Keywords: contrasting structure, moving front, reaction-diffusion equation

UDC: 517.958

MSC: 00A69

DOI: 10.36535/2782-4438-2025-243-56-62