Existence and qualitative properties of multidimensional conical bistable fronts

François Hamel; Régis Monneau; Jean-Michel Roquejoffre

doi:10.3934/dcds.2005.13.1069

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2005, Volume 13, Issue 4: 1069-1096. Doi: 10.3934/dcds.2005.13.1069

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Existence and qualitative properties of multidimensional conical bistable fronts

1.
LATP (UMR CNRS 6632), Faculté des Sciences et Techniques, Université Aix-Marseille III, F-13397 Marseille Cedex 20
2.
CERMICS-ENPC, 6-8 avenue B. Pascal, Cité Descartes, F-77455 Marne-La-Vallée Cedex 2
3.
Laboratoire MIP, Université Paul Sabatier, 31062 Toulouse Cedex 9

Received: September 30, 2004

Revised: January 31, 2005

Published: June 2005

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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.

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