Numerical Investigation of Solutions to a Reaction-diffusion System with Variable Density

Abstract

In this paper we demonstrate the possibilities of the self-similar and approximately self-similar approaches for studying solutions of a nonlinear mutual reaction-diffusion system. The asymptotic behavior of compactly supported solutions and free boundary is studied. Based on established qualitative properties of solutions numerical computation is carried out. The solutions are presented in visualization form, which allows observing evolution of the studied process in time.

Self-similar solutions of a cross-diffusion parabolic system with variable density: explicit estimates and asymptotic behaviour

“…have been discussed by many authors [4][5][6]. Finite speed properties of a perturbation of distribution (FSPD) and the asymptotic behavior of self-similar solutions for another systems are considered in [9][10][11][12].…”