Linear vs. nonlinear selection for the propagation speed of the solutions of scalar reaction-diffusion equations invading an unstable equilibrium

Document Type

Article

Publication Date

5-1-2004

Abstract

We revisit the classical problem of speed selection for the propagation of disturbances in scalar reaction-diffusion equations with one linearly stable and one linearly unstable equilibrium. For a wide class of initial data this problem reduces to finding the minimal speed of the monotone traveling wave solutions connecting these two equilibria in one space dimension. We introduce a variational characterization of these traveling wave solutions and give a necessary and sufficient condition for linear versus nonlinear selection mechanism. We obtain sufficient conditions for the linear and nonlinear selection mechanisms that are easily verifiable. Our method also allows us to obtain efficient lower and upper bounds for the propagation speed. © 2004 Wiley Periodicals, Inc.

Identifier

2442629430 (Scopus)

Publication Title

Communications on Pure and Applied Mathematics

External Full Text Location

https://doi.org/10.1002/cpa.20014

ISSN

00103640

First Page

616

Last Page

636

Issue

5

Volume

57

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