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 and others. The longitudinal variable is treated by means of a result by Weder on dispersion for Schroedinger operators in 1D.

On asymptotic stability in 3D of kinks for the $phi ^4$ model / Cuccagna, Scipio. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - STAMPA. - 360:(2008), pp. 2581-2614.

On asymptotic stability in 3D of kinks for the $phi ^4$ model

CUCCAGNA, Scipio
2008

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 and others. The longitudinal variable is treated by means of a result by Weder on dispersion for Schroedinger operators in 1D.
360
2581
2614
On asymptotic stability in 3D of kinks for the $phi ^4$ model / Cuccagna, Scipio. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - STAMPA. - 360:(2008), pp. 2581-2614.
Cuccagna, Scipio
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

Licenza Creative Commons
I metadati presenti in IRIS UNIMORE sono rilasciati con licenza Creative Commons CC0 1.0 Universal, mentre i file delle pubblicazioni sono rilasciati con licenza Attribuzione 4.0 Internazionale (CC BY 4.0), salvo diversa indicazione.
In caso di violazione di copyright, contattare Supporto Iris

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11380/421723
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 24
  • ???jsp.display-item.citation.isi??? 22
social impact