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. Electronic Journal of Differential Equations, 2007(128), pp. 1-18.
Rights
Attribution 4.0 International