A global nonexistence theorem for viscoelastic equations with arbitrary positive initial energy. (English) Zbl 1173.35575
Summary: We consider the nonlinear viscoelastic equation
\[
u_{tt}-\varDelta u+\int _0^t g(t-\tau)\varDelta u(\tau)\text d\tau+u_t= |u|^{p-1}u \quad \text{in }\varOmega \times (0,\infty)
\]
with Dirichlet boundary conditions. Under some appropriate assumptions on \(g\) and the initial data, a blow-up result with arbitrary positive initial energy is established for \(p< \frac{n}{n-2}\) (if \(n=1,2,\) then \(1<p<\infty \)).
MSC:
| 35L05 | Wave equation |
References:
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