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Blow-up of solutions of a nonlinear viscoelastic wave equation. (English) Zbl 1213.35143

The authors consider a linear viscoelastic problem with a nonlinear source term in polynomial form. They prove a blow up in finite time result for solutions with positive initial energy. By this they extend existing results starting from negative initial energy.

MSC:

35B44 Blow-up in context of PDEs
74D05 Linear constitutive equations for materials with memory
35L20 Initial-boundary value problems for second-order hyperbolic equations
35B40 Asymptotic behavior of solutions to PDEs
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