Global Existence and Asymptotic Behavior for a Coupled System of Viscoelastic Wave Equations with a Delay Term
Year: 2014
Author: Ali Hakem, Mohamed Ferhat, Ali Hakem
Journal of Partial Differential Equations, Vol. 27 (2014), Iss. 4 : pp. 293–317
Abstract
We are interested in the study of a coupled systemof viscoelasticwave equations with a delay term. Firstly global existence of the solutions is proved. The asymptotic behavior is obtained by using multiplier technique proved by A. Guessmia [1], however in the unstable set for certain initial data bolstered with some conditions, we obtain the blow up of the solutions for various sign of initial energy negative, positive or null. We use the same technique in [2] with a necessary modification imposed by our problem. This improves the earlier results in the literature.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v27.n4.2
Journal of Partial Differential Equations, Vol. 27 (2014), Iss. 4 : pp. 293–317
Published online: 2014-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Global existence
Author Details
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Stability and instability results for coupled waves with delay term
Oliveira, Rafael L.
Oquendo, Higidio P.
Journal of Mathematical Physics, Vol. 61 (2020), Iss. 7
https://doi.org/10.1063/1.5144987 [Citations: 6]