Development of the Interfaces for the Nonlinear Reaction-Diffusion equation with Convection
Ugur G. Abdulla, Habeeb Abed Kadhim Aal-Rkhais · IOP Conference Series Materials Science and Engineering · 2019
Abstract 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.