Electron. J. Diff. Eqns.,
Vol. 2007(2007), No. 128, pp. 118.
On the wave equations with memory in noncylindrical domains
Mauro L. Santos
Abstract:
In this paper we prove the exponential and polynomial decays rates
in the case
,
as time approaches infinity of regular solutions
of the wave equations with memory
where
is a non cylindrical domains of
,
.
We show that the dissipation produced by memory effect is
strong enough to produce exponential decay of solution provided
the relaxation function
also decays
exponentially. When the
relaxation function decay polynomially, we show that the solution
decays polynomially with the same rate. For this we introduced a
new multiplier that makes an important role in the obtaining of
the exponential and polynomial decays of the energy of the system.
Existence, uniqueness and regularity of solutions for any
are investigated. The obtained result extends known
results from cylindrical to noncylindrical domains.
Submitted March 8, 2007. Published October 2, 2007.
Math Subject Classifications: 35K55, 35F30, 34B15.
Key Words: Wave equation; noncylindrical domain; memory dissipation.
Show me the
PDF file (298 KB),
TEX file, and other files for this article.

Mauro de Lima Santos
Faculdade de Matemática, Universidade Federal do Pará
Campus Universitario do Guamá,
Rua Augusto Corrêa 01, Cep 66075110, Pará, Brasil
email: ls@ufpa.br 
Return to the EJDE web page