Blow-up of solutions to quasilinear hyperbolic equations with p(x, t)-Laplacian and positive initial energy

The aim of this paper is to study an initial and homogeneous boundary value problem to a quasilinear hyperbolic equation with a p(x, t)-Laplacian and a positive initial energy. The authors prove that the solution blows up in a finite time under some conditions on the initial value, the exponents and the coefficients in the equation. The results generalize and improve that of S.N. Antonsev (2011) [6]. Besides, the conditions of positivity of the integral to the initial data and the boundedness of p(t)(x, t) are removed. (c) 2014 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.