Development of the Interfaces for the Nonlinear Reaction-Diffusion equation with Convection

2nd International Scientific Conference (Pure Sciences, Brilliant Creativity and Renewed Building)

Abdulla, Ugur G.^1 ; Aal-Rkhais, Habeeb A.^2

Department of Mathematics, Florida Institute of Technology, Melbourne

FL, United States^1

Department of Mathematics, College of Computer Science and Mathematics, Thi-Qar University, Iraq^2

关键词: Compactly supported;    Initial development;    Initial functions;    Non-linear scaling;    Nonlinear reaction;    Nonlinear reaction-diffusion equations;    Parabolic PDEs;    Relative strength;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/571/1/012012/pdf
DOI  :  10.1088/1757-899X/571/1/012012

来源: IOP

【 摘 要 】

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.