Global exponential convergence to variational traveling waves in cylinders

C. B. Muratov, M. Novaga

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)293-315
Number of pages23
JournalSIAM Journal on Mathematical Analysis
Volume44
Issue number1
DOIs
StatePublished - 2012

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

Keywords

  • Exponentially weighted spaces
  • Front propagation
  • Front selection
  • Nonlinear stability
  • Reaction-diffusion equations

Fingerprint Dive into the research topics of 'Global exponential convergence to variational traveling waves in cylinders'. Together they form a unique fingerprint.

Cite this