Abstract
This paper deals with a class of nonlinear viscoelastic wave equation with damping and source terms ${u_{tt}} - \Delta u - \Delta {u_t} - \Delta {u_{tt}} + \int_0^t {g(t - s)\Delta u(s)ds + {u_t}{u_t}{^{m - 2}} = u|u|{^{p - 2}}} $ with acoustic boundary conditions. Under some appropriate assumption on relaxation function g and the initial data, we prove that the solution blows up in finite time if the positive initial energy satisfies a suitable condition.
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