Contributions to Nonlinear Analysis
Produktnummer:
18e83fd1362ddb4024bfda8b297a07488b
| Themengebiete: | Maxwell's equations Nonlinear equations Partial differential equations calculus hyperbolic equation partial differential equation wave equation |
|---|---|
| Veröffentlichungsdatum: | 18.11.2005 |
| EAN: | 9783764371494 |
| Sprache: | Englisch |
| Seitenzahl: | 520 |
| Produktart: | Gebunden |
| Herausgeber: | Cazenave, Thierry Costa, David Lopes, Orlando Manásevich, Raúl Rabinowitz, Paul Ruf, Bernhard Tomei, Carlos |
| Verlag: | Springer Basel |
| Untertitel: | A Tribute to D.G. de Figueiredo on the Occasion of his 70th Birthday |
Produktinformationen "Contributions to Nonlinear Analysis"
This paper is concerned with the existence and uniform decay rates of solutions of the waveequation with a sourceterm and subject to nonlinear boundary damping ? ? u ?? u =|u| u in ? ×(0,+?) ? tt ? ? ? ? u=0 on ? ×(0,+?) 0 (1. 1) ? ? u+g(u)=0 on ? ×(0,+?) ? t 1 ? ? ? ? 0 1 u(x,0) = u (x); u (x,0) = u (x),x? ? , t n where ? is a bounded domain of R ,n? 1, with a smooth boundary ? = ? ?? . 0 1 Here, ? and ? are closed and disjoint and ? represents the unit outward normal 0 1 to ?. Problems like (1. 1), more precisely, ? u ?? u =?f (u)in? ×(0,+?) ? tt 0 ? ? ? ? u=0 on ? ×(0,+?) 0 (1. 2) ? ? u =?g(u )?f (u)on? ×(0,+?) ? t 1 1 ? ? ? ? 0 1 u(x,0) = u (x); u (x,0) = u (x),x? ? , t were widely studied in the literature, mainly when f =0,see[6,13,22]anda 1 long list of references therein. When f =0and f = 0 this kind of problem was 0 1 well studied by Lasiecka and Tataru [15] for a very general model of nonlinear functions f (s),i=0,1, but assuming that f (s)s? 0, that is, f represents, for i i i each i, an attractive force.
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