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Theoretical and Applied Mechanics, 2020, Volume 47, Issue 1, Pages 123–154
DOI: https://doi.org/10.2298/TAM200428008P (Mi tam80) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Local existence and blow-up of solutions for coupled viscoelastic wave equations with degenerate damping terms

Erhan Pişkina, Fatma Ekincia, Khaled Zennirb

a Department of Mathematics, Dicle University, Turkey
b Department of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass, Saudi Arabia
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DOI: https://doi.org/10.2298/TAM200428008P
Abstract: In this paper, we investigate a nonlinear system of viscoelastic equations with degenerate damping and source terms in a bounded domain. Under appropriate assumptions on the parameters, degenerate damping terms and the relaxation functions $\varpi_i$, $(i=1,2)$, we prove local existence and uniqueness of the solution by using the Faedo–Galerkin method with a new scenario. Then, we prove the blow-up of weak solutions to problem (1.1). This improves earlier results in the literature [6,23,25].
Keywords: local existence, blow-up, viscoelastic wave equations, degenerate damping.
Received: 28.04.2020
Revised: 28.05.2020
Bibliographic databases:
Document Type: Article
MSC: 35B40, 35B44, 35L05, 35L75
Language: English
Citation: Erhan Pişkin, Fatma Ekinci, Khaled Zennir, “Local existence and blow-up of solutions for coupled viscoelastic wave equations with degenerate damping terms”, Theor. Appl. Mech., 47:1 (2020), 123–154
Citation in format AMSBIB
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\by Erhan~Pi{\c s}kin, Fatma~Ekinci, Khaled~Zennir
\paper Local existence and blow-up of solutions for coupled viscoelastic wave equations with degenerate damping terms
\jour Theor. Appl. Mech.
\yr 2020
\vol 47
\issue 1
\pages 123--154
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\crossref{https://doi.org/10.2298/TAM200428008P}
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    • This publication is cited in the following 7 articles:
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