Contributions to Nonlinear Analysis | A Tribute to D.G. de Figueiredo on the Occasion of his 70th Birthday | ISBN 9783764374013

Contributions to Nonlinear Analysis

A Tribute to D.G. de Figueiredo on the Occasion of his 70th Birthday

herausgegeben von Thierry Cazenave und weiteren
Mitwirkende
Herausgegeben vonThierry Cazenave
Herausgegeben vonDavid Costa
Herausgegeben vonOrlando Lopes
Herausgegeben vonRaúl Manásevich
Herausgegeben vonPaul Rabinowitz
Herausgegeben vonBernhard Ruf
Herausgegeben vonCarlos Tomei
Buchcover Contributions to Nonlinear Analysis  | EAN 9783764374013 | ISBN 3-7643-7401-2 | ISBN 978-3-7643-7401-3
Leseprobe

Contributions to Nonlinear Analysis

A Tribute to D.G. de Figueiredo on the Occasion of his 70th Birthday

herausgegeben von Thierry Cazenave und weiteren
Mitwirkende
Herausgegeben vonThierry Cazenave
Herausgegeben vonDavid Costa
Herausgegeben vonOrlando Lopes
Herausgegeben vonRaúl Manásevich
Herausgegeben vonPaul Rabinowitz
Herausgegeben vonBernhard Ruf
Herausgegeben vonCarlos Tomei
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.