Reaction–diffusion equations with nonlinear boundary conditions in narrow domains

Article type: Research Article

Authors: Freidlin, Mark | Spiliopoulos, Konstantinos

Affiliations: Department of Mathematics, University of Maryland, College Park, MD 20742, USA. E-mails: {mif, kspiliop}@math.umd.edu

Note: [] Corresponding author.

Abstract: Second initial boundary problem in narrow domains of width ε�1 for linear second-order differential equations with nonlinear boundary conditions is considered in this paper. Using probabilistic methods we show that the solution of such a problem converges as ε↓0 to the solution of a standard reaction–diffusion equation in a domain of reduced dimension. This reduction allows to obtain some results concerning wave front propagation in narrow domains. In particular, we describe conditions leading to jumps of the wave front.

Keywords: reaction–diffusion equations, narrow domains, wave front propagation, instantaneous reflection

DOI: 10.3233/ASY-2008-0894

Journal: Asymptotic Analysis, vol. 59, no. 3-4, pp. 227-249, 2008