Existence and qualitative properties of multidimensional conical bistable fronts

Pages: 1069 - 1096, Volume 13, Issue 4, November 2005

doi:10.3934/dcds.2005.13.1069       Abstract        Full Text (419.1K)       Related Articles

François Hamel - LATP (UMR CNRS 6632), Faculté des Sciences et Techniques, Université Aix-Marseille III, F-13397 Marseille Cedex 20, France (email)
Régis Monneau - CERMICS-ENPC, 6-8 avenue B. Pascal, Cité Descartes, F-77455 Marne-La-Vallée Cedex 2, France (email)
Jean-Michel Roquejoffre - Laboratoire MIP, Université Paul Sabatier, 31062 Toulouse Cedex 9, France (email)

Abstract: Travelling fronts with conical-shaped level sets are constructed for reaction-diffusion equations with bistable nonlinearities of positive mass. The construction is valid in space dimension 2, where two proofs are given, and in arbitrary space dimensions under the assumption of cylindrical symmetry. General qualitative properties are presented under various assumptions: conical conditions at infinity, existence of a sub-level set with globally Lipschitz boundary, monotonicity in a given direction.

Keywords:  Conical travelling fronts, bistable elliptic equations.
Mathematics Subject Classification:  35B05, 35B50, 35J99.

Received: October 2004;      Revised: February 2005;      Published: August 2005.