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Generalized Transition Waves and Their Properties
Author(s) -
Berestycki Henri,
Hamel François
Publication year - 2012
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.21389
Subject(s) - uniqueness , monotonic function , geodesic , planar , mathematics , robustness (evolution) , cover (algebra) , reaction–diffusion system , mathematical analysis , pure mathematics , computer science , mechanical engineering , biochemistry , chemistry , computer graphics (images) , engineering , gene
In this paper, we generalize the usual notions of waves, fronts, and propagation speeds in a very general setting. These new notions, which cover all usual situations, involve uniform limits, with respect to the geodesic distance, to a family of hypersurfaces that are parametrized by time. We prove the existence of new such waves for some time‐dependent reaction‐diffusion equations, as well as general intrinsic properties, some monotonicity properties, and some uniqueness results for almost‐planar fronts. The classification results, which are obtained under some appropriate assumptions, show the robustness of our general definitions. © 2012 Wiley Periodicals, Inc.