On asymptotic stability in 3D of kinks for the 𝜙⁴ model-Reference-Cited by-同舟云学术

On asymptotic stability in 3D of kinks for the 𝜙⁴ model

Published:2007-11-28 Issue:5 Volume:360 Page:2581-2614
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Cuccagna Scipio

Abstract

We add to a kink, which is a 1 dimensional structure, two transversal directions. We then check its asymptotic stability with respect to compactly supported perturbations in 3D and a time evolution under a Nonlinear Wave Equation (NLW). The problem is inspired by work by Jack Xin on asymptotic stability in dimension larger than 1 of fronts for reaction diffusion equations. The proof involves a separation of variables. The transversal variables are treated as in work on Nonlinear Klein Gordon Equation (NLKG) originating from Klainerman and from Shatah in a particular elaboration due to Delort et al. The longitudinal variable is treated by means of a result by Weder on dispersion for Schrödinger operators in 1D.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/2008-360-05/S0002-9947-07-04356-5/S0002-9947-07-04356-5.pdf

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3. [DFX] Delort, Fang, Xue, Global existence of small solutions for quadratic quasilinear Klein Gordon systems in two space dimensions, preprint.

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