Geodesic
Local existence and blow-up of solutions for coupled viscoelastic wave equations with degenerate damping terms
Theoretical and applied mechanics, Tome 47 (2020) no. 1, p. 123

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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].
DOI : 10.2298/TAM200428008P
Classification : 35B40, 35B44, 35L05, 35L75
Keywords: local existence, blow-up, viscoelastic wave equations, degenerate damping 
Erhan Pişkin; Fatma Ekinci; Khaled Zennir. Local existence and blow-up of solutions for coupled viscoelastic wave equations with degenerate damping terms. Theoretical and applied mechanics, Tome 47 (2020) no. 1, p. 123 . doi: 10.2298/TAM200428008P
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