A blow-up result for a nonlinear wave equation with variable-exponent nonlinearities

In this paper, we consider the following wave equation: u(tt) - div(|u| m(x)-2u) + ut = | u| p( x)- 2u in which is a nonnegative constant and the exponents of nonlinearity m(x), p(x) are given functions. For arbitrary positive initial energy, we prove a finite-time blow-up result.