On asymptotic stability of moving kink for relativistic Ginzburg-Landau equation

Details On asymptotic stability of moving kink for relativistic Ginzburg-Landau equation On asymptotic stability of moving kink for relativistic Ginzburg-Landau equation

2009-10-29

arxiv.org/abs/0910.5538v2

Mathematics

Analysis of PDEs

30 pages, 0 figures

Scientific paper

We prove the asymptotic stability of the moving kinks for the nonlinear relativistic wave equations in one space dimension with a Ginzburg-Landau potential: starting in a small neighborhood of the kink, the solution, asymptotically in time, is the sum of a uniformly moving kink and dispersive part described by the free Klein-Gordon equation. The remainder decays in a global energy norm. Crucial role in the proofs play our recent results on the weighted energy decay for the Klein-Gordon equations.

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