On the wave equations with memory in noncylindrical domains
Date
2007-10-02
Authors
Santos, Mauro de Lima
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
In this paper we prove the exponential and polynomial decays rates in the case n > 2, as time approaches infinity of regular solutions of the wave equations with memory
utt - Δu + ∫t0 g(t - s) Δu(s)ds = 0 in Q̂
where Q̂ is a non cylindrical domains of ℝn+1, (n ≥ 1). We show that the dissipation produced by memory effect is strong enough to produce exponential decay of solution provided the relaxation function g 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 n ≥ 1 are investigated. The obtained result extends known results from cylindrical to non-cylindrical domains.
Description
Keywords
Wave equation, Noncylindrical domain, Memory dissipation
Citation
Santos, M. D. L. (2007). On the wave equations with memory in noncylindrical domains. <i>Electronic Journal of Differential Equations, 2007</i>(128), pp. 1-18.
Rights
Attribution 4.0 International