Global convergence toward traveling fronts in nonlinear parabolic systems with a gradient structure
In: Annales de l'Institut Henri Poincaré. Analyse non linéaire, Jg. 25 (2008), Heft 2, S. 381-424
Online
academicJournal
- print, 30 ref
We consider nonlinear parabolic systems of the form ut = -∇V(u) + uxx, where u εRn,n ≥ 1, x ε R, and the potential V is coercive at infinity. For such systems, we prove a result of global convergence toward bistable fronts which states that invasion of a stable homogeneous equilibrium (a local minimum of the potential) necessarily occurs via a traveling front connecting to another (lower) equilibrium. This provides, for instance, a generalization of the global convergence result obtained by Fife and McLeod [P. Fife, J.B. McLeod, The approach of solutions of nonlinear diffusion equations to traveling front solutions, Arch. Rat. Mech. Anal. 65 (1977) 335-361] in the case n = 1. The proof is based purely on energy methods, it does not make use of comparison principles, which do not hold any more when n > 1.
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Global convergence toward traveling fronts in nonlinear parabolic systems with a gradient structure
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Autor/in / Beteiligte Person: | RISLER, Emmanuel |
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Zeitschrift: | Annales de l'Institut Henri Poincaré. Analyse non linéaire, Jg. 25 (2008), Heft 2, S. 381-424 |
Veröffentlichung: | Paris: Elsevier, 2008 |
Medientyp: | academicJournal |
Umfang: | print, 30 ref |
ISSN: | 0294-1449 (print) |
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