Exponential Decay for the Solution of Semilinear Viscoelastic Wave Equations with Localized Damping
dc.contributor.author | Cavalcanti, Marcelo M. ( ) | |
dc.contributor.author | Domingos Cavalcanti, V. N. ( ![]() | |
dc.contributor.author | Soriano, Juan A. ( ) | |
dc.date.accessioned | 2020-08-07T20:40:33Z | |
dc.date.available | 2020-08-07T20:40:33Z | |
dc.date.issued | 2002-05-22 | |
dc.identifier.citation | Cavalcanti, M. M., Domingos Cavalcanti, V. N., & Soriano, J. A. (2002). Exponential decay for the solution of semilinear viscoelastic wave equations with localized damping. Electronic Journal of Differential Equations, 2002(44), pp. 1-14. | en_US |
dc.identifier.issn | 1072-6691 | |
dc.identifier.uri | https://digital.library.txstate.edu/handle/10877/12343 | |
dc.description.abstract | In this paper we obtain an exponential rate of decay for the solution of the viscoelastic nonlinear wave equation utt - Δu + ƒ(x, t, u) + ∫t0 g(t - T) Δu(T) dT + α(x)ut = 0 in Ω x (0,∞). Here the damping term a(x)ut may be null for some part of the domain Ω. 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. | en_US |
dc.format | Text | |
dc.format.extent | 14 pages | |
dc.format.medium | 1 file (.pdf) | |
dc.language.iso | en | en_US |
dc.publisher | Southwest Texas State University, Department of Mathematics | en_US |
dc.source | Electronic Journal of Differential Equations, 2002, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
dc.subject | Semilinear wave equation | en_US |
dc.subject | Memory | en_US |
dc.subject | Localized damping | en_US |
dc.title | Exponential Decay for the Solution of Semilinear Viscoelastic Wave Equations with Localized Damping | en_US |
dc.type | publishedVersion | |
txstate.documenttype | Article | |
dc.rights.license | ![]() This work is licensed under a Creative Commons Attribution 4.0 International License. | |
dc.description.department | Mathematics |