Journal
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
Volume 65, Issue 5, Pages 592-648Publisher
WILEY
DOI: 10.1002/cpa.21389
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Funding
- French Agence Nationale de la Recherche [ANR 08-BLAN-0313]
- National Science Foundation FRG [DMS-1065979]
- Alexander von Humboldt Foundation
- Agence Nationale de la Recherche (ANR) [ANR-08-BLAN-0313] Funding Source: Agence Nationale de la Recherche (ANR)
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1065979] Funding Source: National Science Foundation
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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. (c) 2012 Wiley Periodicals, Inc.
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