Boundary Layer for Chaffee-Infante Type Equation

Roger Temam and Xiaoming Wang

Address. R. Temam, The Institute for Scientific Computing & Applied Mathematics, Indiana University, Rawles Hall, Bloomington, IN 47405

X. Wang, Laboratoire d'Analyse Numerique, Universite Paris-Sud, Batiment 425, 91405 Orsay, France

Current Address: Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012, on leave from Department of Mathematics, Iowa State University, Ames, IA 50011


Abstract. This article is concerned with the nonlinear singular perturbation problem due to small diffusivity in nonlinear evolution equations of Chaffee-Infante type. The boundary layer appearing at the boundary of the domain is fully described by a corrector which is ``explicitly" constructed. This corrector allows us to obtain convergence in Sobolev spaces up to the boundary.

AMS classification. 35B40, 35C20, 35Q30, 46N20, 76D10

Key words. Boundary layers, correctors, nonlinear reaction diffusion equations, chaffee-infante equation