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Blow-up of solution for nonlinear viscoelastic wave equation. (Chinese. English summary) Zbl 1374.35085

Summary: The existence and blow-up of the solution for a viscoelastic wave equation with nonlinear damping and source terms were considered. Especially, the coefficient of the principal part of the equation \(\mu \left(t \right)\) was time \(t\) dependent function. Under some assumptions, the existence of local solution was proved. When the initial energy has an upper bound and the local solution exists, the solution blows up in finite time by using the potential well theory and energy method. In addition, an estimate about the blow-up time of the solution was obtained.

MSC:

35B44 Blow-up in context of PDEs
35L05 Wave equation
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