Exponential decay for the solution of semilinear viscoelastic wave equations with localized damping
| Autor: | Marcelo M. Cavalcanti, Valeria N. Domingos Cavalcanti, Juan A. Soriano |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2002 |
| Předmět: | |
| Zdroj: | Electronic Journal of Differential Equations, Vol 2002, Iss 44, Pp 1-14 (2002) |
| Druh dokumentu: | article |
| ISSN: | 1072-6691 81713894 |
| Popis: | In this paper we obtain an exponential rate of decay for the solution of the viscoelastic nonlinear wave equation $$ u_{tt}-Delta u+f(x,t,u)+int_0^tg(t-au )Delta u( au ),dau +a(x)u_t=0quad hbox{in }Omegaimes (0,infty ). $$ Here the damping term $a(x)u_t$ may be null for some part of the domain $Omega$. By assuming that the kernel $g$ in the memory term decays exponentially, the damping effect allows us to avoid compactness arguments and and to reduce number of the energy estimates considered in the prior literature. We construct a suitable Liapunov functional and make use of the perturbed energy method. |
| Databáze: | Directory of Open Access Journals |
| Externí odkaz: |
|