Reaction Diffusion Equations with Nonlinear Boundary Conditions in Narrow Domains

Mark Freidlin; Konstantinos Spiliopoulos

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arXiv · 1005.2505

Reaction Diffusion Equations with Nonlinear Boundary Conditions in Narrow Domains

Mark Freidlin·Konstantinos Spiliopoulos

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Abstract

Second initial boundary problem in narrow domains of width $ε\ll 1$ 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 $ε\downarrow 0$ 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.

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Mark Freidlin, Konstantinos Spiliopoulos. 2010-05-14. Reaction Diffusion Equations with Nonlinear Boundary Conditions in Narrow Domains. https://arxiv.org/abs/1005.2505

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