Heteroclinic travelling waves of gradient diffusion systems

Fecha: Vie, Oct 30 2009

Hora: 12:30

Ubicación: Bizkaia Technology Park, Building 500 E-48160 DERIO - Basque Country- Spain

Ponentes: Nick Alikakos

We establish existence of travelling waves to the gradient system ut = uzz −∇W(u) connecting two minima of W when u : R×(0,∞) −→ RN, that is, we establish existence of a pair (U, c) ∈ [C2 (R)]N × (0, ∞), satisfying

Uxx − ∇W (U ) = −c Ux U(±∞) = a±,

where a± are local minima of the potential W ∈ C2loc (RN) with W(a) < W(a+) = 0 and N ≥ 1. Our method is variational and based on the minimization of the functional Ec(U) = ∫R {1/2|Ux|2 +W(U)} ecx dx in the appropriate space setup. Following Alikakos-Fusco [A-F], we introduce an artificial constraint to restore compactness and force the desired asymptotic behavior, which we later remove. We provide variational characterizations of the traveling wave and the speed. In particular, we show that Ec(U) = 0.

Ponentes confirmados:

Nick Alikakos