On the wave equations with memory in noncylindrical domains
| dc.contributor.author | Santos, Mauro de Lima | |
| dc.date.accessioned | 2021-08-17T16:39:02Z | |
| dc.date.available | 2021-08-17T16:39:02Z | |
| dc.date.issued | 2007-10-02 | |
| dc.description.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. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 18 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.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. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14342 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University-San Marcos, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2007, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. | |
| dc.subject | Wave equation | |
| dc.subject | Noncylindrical domain | |
| dc.subject | Memory dissipation | |
| dc.title | On the wave equations with memory in noncylindrical domains | |
| dc.type | Article |