Abstract
In this paper, we study the following nonlinear thermo-viscoelastic system utt−Δu+∫0tg(t−s)Δu(s)ds+v=|u|p(x)−2u,vt−Δv=ut,in a bounded domain Ω⊂Rn. By employing the modified potential well theory, we discuss the properties of global existence and finite time blow-up of the solutions of the problem. Moreover, in the former case by constructing a suitable Lyapunov functional we prove the exponential decay for solutions and in the latter one we give the lower and upper bounds for blow-up time of the blow-up solutions.
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