Lower bounds for the blow-up time to a nonlinear viscoelastic wave equation with strong damping

Abstract

This paper deals with a nonlinear viscoelastic wave equation with strong damping. By the means of the interpolation inequalities and differential inequality technique, we obtain a lower bound for blow-up time of the solution. This result extends our earlier work Peng et al. [Appl. Math. Lett., 76, 2018].