Global exponential convergence to variational traveling waves in cylinders

Document Type

Article

Publication Date

5-28-2012

Abstract

We prove, under generic assumptions, that the special variational traveling wave that minimizes the exponentially weighted Ginzburg-Landau functional associated with scalar reactiondiffusion equations in infinite cylinders is the long-time attractor for the solutions of the initial value problems with front-like initial data. The convergence to this traveling wave is exponentially fast. The obtained result is mainly a consequence of the gradient flow structure of the considered equation in the exponentially weighted spaces and does not depend on the precise details of the problem. It strengthens our earlier generic propagation and selection result for ̀pushed̀ fronts. © 2012 Society for Industrial and Applied Mathematics.

Identifier

84861416000 (Scopus)

Publication Title

SIAM Journal on Mathematical Analysis

External Full Text Location

https://doi.org/10.1137/110833269

ISSN

00361410

First Page

293

Last Page

315

Issue

1

Volume

44

Grant

0908279

Fund Ref

National Science Foundation

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