On asymptotic stability in 3D of kinks for the $ϕ^4$ model
| dc.creator | Cuccagna, Scipio | |
| dc.date | 2008-01-17 | |
| dc.date.accessioned | 2026-07-07T08:55:01Z | |
| dc.date.available | 2026-07-07T08:55:01Z | |
| dc.description | 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. | |
| dc.description | To appear on Transactions of the American Mathematical Society | |
| dc.identifier | https://arxiv.org/abs/0801.2678 | |
| dc.identifier | http://arxiv.org/abs/0801.2678 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146146 | |
| dc.subject | Analysis of PDEs | |
| dc.title | On asymptotic stability in 3D of kinks for the $ϕ^4$ model | |
| dc.type | text |