Open AccessDevelopment of the Interfaces for the Nonlinear Reaction-Diffusion equation with Convection
Author(s) -
Ugur G. Abdulla,
Habeeb A. Aal-Rkhais
Publication year - 2019
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/571/1/012012
Subject(s) - diffusion , convection , advection , convection–diffusion equation , nonlinear system , focus (optics) , absorption (acoustics) , interface (matter) , mechanics , function (biology) , mathematical analysis , mathematics , statistical physics , physics , thermodynamics , optics , bubble , quantum mechanics , maximum bubble pressure method , evolutionary biology , biology
We study the initial development and asymptotics of the interfaces and local solutions near the interfaces for the nonlinear reaction diffusion convection equation with compactly supported initial function. Depending on the relative strength of three competing terms such as diffusion, advection or absorption, the interface may shrink, expand or remain stationary. In this paper we focus only on two cases when the diffusion dominates and the interface expands and the other case when absorption term dominates and the interface shrinks. The significant methods that we used are rescaling and blow-up techniques.