Abstract: We considered estimate of a  lower bound of blow-up time for solutions to  a class of nonlinear viscoelastic hyperbolic equations involving  supercritical source terms. By constructing the control function with damping term, using the mehtod of energy estimate  and Sobolev embedding theorem, we obtained an explicit estimate of lower bound of the blow-up time  for the solutions to the problem.

Key words: viscoelastic hyperbolic equation, method of energy estimate, estimate of lower bound, blow-up time