Traveling fronts bifurcating from stable layers in the presence of conservation laws

Alin Pogan, Arnd Scheel

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We study traveling waves bifurcating from stable standing layers in systems where a reaction-diffusion equation couples to a scalar conservation law. We prove the existence of weekly decaying traveling fronts that emerge in the presence of a weakly stable direction on a center manifold. Moreover, we show the existence of bifurcating traveling waves of constant mass. The main difficulty is to prove the smoothness of the ansatz in exponentially weighted spaces required to apply the Lyapunov-Schmidt methods.

Original languageEnglish (US)
Pages (from-to)2619-2651
Number of pages33
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume37
Issue number5
DOIs
StatePublished - May 2017

Keywords

  • Bifurcation
  • Conservation law
  • Far-field corrections
  • Lyapunov-Schmidt reduction
  • Traveling waves

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