Erhan Piskin, A lower bound for the blow up time of a system of viscoelastic wave equations with nonlinear damping and source terms, Vol. 2017 (2017), Article ID 3, pp. 1-9

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DOI: 10.23952/jnfa.2017.3

Received August 1, 2016; Accepted November 15, 2016

Abstract. In this paper, we consider the blow up of an initial and boundary value problem for a system of viscoelastic wave equations
$u_{tt}-\bigtriangleup u+\int\nolimits_{0}^{t}g_{1}\left( t-\tau \right)\bigtriangleup u\left( \tau \right) d\tau +\left\vert u_{t}\right\vert^{p-1}u_{t}=f_{1}\left( u,v\right),$ $v_{tt}-\bigtriangleup v+\int\nolimits_{0}^{t}g_{2}\left( t-\tau \right)\bigtriangleup v\left( \tau \right) d\tau +\left\vert v_{t}\right\vert^{q-1}v_{t}=f_{2}\left( u,v\right) .$
Lower bounds for the blow up time of the blow up solutions is given.