Calculus of Variations and Geometric Measure Theory
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M. Lucia - C. Muratov - M. Novaga

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

created on 05 May 2003
modified by novaga on 04 Apr 2016


Published Paper

Inserted: 5 may 2003
Last Updated: 4 apr 2016

Journal: Comm. Pure Appl. Math.
Volume: 57
Number: 5
Pages: 616-636
Year: 2004


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 vs. nonlinear selection mechanism. Easily verifiable sufficient conditions for the linear and nonlinear selection mechanisms are obtained. Our method also allows to obtain efficient lower and upper bounds for the propagation speed.


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