Boundary layer analysis of nonlinear reaction-diffusion equations in a smooth domain

Advances in Nonlinear Analysis

卷:6

Jung Chang-Yeol¹  Park Eunhee²  Temam Roger² 

[1] Department of Mathematical Sciences, School of Natural Science,Ulsan National Institute of Science and Technology, Ulsan, Republic of Korea;

[2] Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, Indiana, USA;

关键词: boundary layers;    singular perturbations;    reaction-diffusion;    boundary fitted coordinates;    35b25;    35c20;    76d10;    35k05;   

DOI  :  10.1515/anona-2015-0148

来源: DOAJ

【 摘 要 】

In this article, we consider a singularly perturbed nonlinear reaction-diffusion equation whose solutions display thin boundary layers near the boundary of the domain. We fully analyse the singular behaviours of the solutions at any given order with respect to the small parameter ε, with suitable asymptotic expansions consisting of the outer solutions and of the boundary layer correctors. The systematic treatment of the nonlinear reaction terms at any given order is novel along the singular perturbation analysis. We believe that the analysis can be suitably extended to other nonlinear problems.

【 授权许可】

Unknown