Features of the moving-front solution for a two-dimensional problem with a discontinuous cubic nonlinearity

E. A. Chunzhuk

Lomonosov Moscow State University

Abstract: In this paper, we examine solutions of the moving-front-type for a two-dimensional reaction-diffusion equation with cubic nonlinearity and propose a method for obtaining asymptotic approximations of moving fronts propagating in a medium with discontinuous characteristics is presented. The basic features arising in solving the two-dimensional problem are discussed.

Keywords: reaction-diffusion type equation, discontinuous cubic nonlinearity, moving front, small parameter, asymptotic approximation

UDC: 517.955.8

MSC: 35C20

DOI: 10.36535/2782-4438-2025-243-81-89