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

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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].
Keywords: local existence, blow-up, viscoelastic wave equations, degenerate damping 
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     author = {Erhan Pi\c{s}kin and Fatma Ekinci and Khaled Zennir},
     title = {Local existence and blow-up of solutions for coupled viscoelastic wave equations with degenerate damping terms},
     journal = {Theoretical and applied mechanics},
     pages = {123 - 154},
     publisher = {mathdoc},
     volume = {47},
     number = {1},
     year = {2020},
     url = {http://geodesic.mathdoc.fr/item/TAM_2020_47_1_a9/}
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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. http://geodesic.mathdoc.fr/item/TAM_2020_47_1_a9/