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Bistable traveling waves around an obstacle
Author(s) -
Berestycki Henri,
Matano Hiroshi,
Hamel François
Publication year - 2009
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20275
Subject(s) - obstacle , bistability , planar , uniqueness , front (military) , traveling wave , mathematics , nonlinear system , mathematical analysis , infinity , space (punctuation) , geometry , physics , law , computer science , computer graphics (images) , quantum mechanics , meteorology , political science , operating system
We consider traveling waves for a nonlinear diffusion equation with a bistable or multistable nonlinearity. The goal is to study how a planar traveling front interacts with a compact obstacle that is placed in the middle of the space ℝ N . As a first step, we prove the existence and uniqueness of an entire solution that behaves like a planar wave front approaching from infinity and eventually reaching the obstacle. This causes disturbance on the shape of the front, but we show that the solution will gradually recover its planar wave profile and continue to propagate in the same direction, leaving the obstacle behind. Whether the recovery is uniform in space is shown to depend on the shape of the obstacle. © 2008 Wiley Periodicals, Inc.