Existence and blow up for viscoelastic hyperbolic equations with variable exponents - Ying Chu; Bo Wen; Libo Cheng (Communications in Analysis and Mechanics)
In this article, we consider a nonlinear viscoelastic hyperbolic problem with variable exponents. By using the Faedo$ - $Galerkin method and the contraction mapping principle, we obtain the existence of weak solutions under suitable assumptions on the variable exponents $ m(x) $ and $ p(x) $. Then we prove that a solution blows up in finite time with positive initial energy as well as nonpositive initial energy.