Traveling Waves with Multiple and Nonconvex Fronts for a Bistable Semilinear Parabolic Equation

Manuel Del Pino, Michal Kowalczyk, Juncheng Wei

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

We construct new examples of traveling wave solutions to the bistable and balanced semilinear parabolic equation in. Our first example is that of a traveling wave solution with two non planar fronts that move with the same speed. Our second example is a traveling wave solution with a nonconvex moving front. To our knowledge no existence results of traveling fronts with these type of geometric characteristics have been previously known. Our approach explores a connection between solutions of the semilinear parabolic PDE and eternal solutions to the mean curvature flow in.

Original languageEnglish
Pages (from-to)481-547
Number of pages67
JournalCommunications on Pure and Applied Mathematics
Volume66
Issue number4
DOIs
Publication statusPublished - 1 Apr 2013

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this