On asymptotic stability in 3D of kinks for the model

Author:
Scipio Cuccagna

Journal:
Trans. Amer. Math. Soc. **360** (2008), 2581-2614

MSC (2000):
Primary 35L70, 37K40, 35B40

Published electronically:
November 28, 2007

MathSciNet review:
2373326

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Abstract | References | Similar Articles | Additional Information

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.

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Additional Information

**Scipio Cuccagna**

Affiliation:
Dipartimento di Scienze e Metodi per l’Ingegneria, Università di Modena e Reggio Emilia, Padiglione Morselli, via Amendola 2, Reggio Emilia 42100, Italy

Email:
cuccagna.scipio@unimore.it

DOI:
http://dx.doi.org/10.1090/S0002-9947-07-04356-5

Received by editor(s):
June 28, 2004

Received by editor(s) in revised form:
November 30, 2005, and March 5, 2006

Published electronically:
November 28, 2007

Additional Notes:
This research was fully supported by a special grant from the Italian Ministry of Education, University and Research.

Article copyright:
© Copyright 2007
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.