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

Global exponential convergence to variational traveling waves in cylinders

created by novaga on 08 Dec 2011
modified on 15 May 2016


Published Paper

Inserted: 8 dec 2011
Last Updated: 15 may 2016

Journal: SIAM J. on Math. Anal.
Volume: 44
Number: 1
Pages: 293-315
Year: 2012


We prove, under generic assumptions, that the special variational traveling wave that minimizes the exponentially weighted Ginzburg-Landau functional associated with scalar reaction-diffusion 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 “pushed” fronts.


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