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 ϖi, (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.
\Bibitem{PisEkiZen20}
\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
\mathnet{http://mi.mathnet.ru/tam80}
\crossref{https://doi.org/10.2298/TAM200428008P}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85089271027}
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This publication is cited in the following 7 articles:
Mohammad Shahrouzi, Jorge Ferreira, Faramarz Tahamtani, “Coupled system of nonlinear viscoelastic plate equations of (p(x),q(x))‐Kirchhoff‐type: Global existence, general decay, and blow‐up”, Math Methods in App Sciences, 47:4 (2024), 2472
Fatma EKİNCİ, Erhan PİŞKİN, “Blow up and Exponential Growth to a Kirchhoff-Type Viscoelastic Equation with Degenerate Damping Term”, Mathematical Sciences and Applications E-Notes, 11:3 (2023), 153
Fatma EKİNCİ, Erhan PİŞKİN, “Stability of Solutions for a Krichhoff-Type Plate Equation with Degenerate Damping”, Communications in Advanced Mathematical Sciences, 5:3 (2022), 131
Fatma Ekinci, Erhan Pişkin, Khaled Zennir, “Existence, blow up and growth of solutions for a coupled quasi-linear viscoelastic Petrovsky equations with degenerate damping terms”, Journal of Information and Optimization Sciences, 43:4 (2022), 705
Erhan Pişkin, Fatma Ekinci, “Global existence of solutions for a coupled viscoelastic plate equation with degenerate damping terms”, Tbilisi Math. J., 14:3 (2021)
Yousif Altayeb, “New scenario of decay rate for system of three nonlinear wave equations with visco-elasticities”, AIMS Mathematics, 6:7 (2021), 7251
Fatma Ekinci, Erhan Pișkin, Salah Mahmoud Boulaaras, Ibrahim Mekawy, Yuanfang Ru, “Global Existence and General Decay of Solutions for a Quasilinear System with Degenerate Damping Terms”, Journal of Function Spaces, 2021 (2021), 1
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