Antontsev S.Wave Equation with p(x,t)- Laplacian and Damping Term: Existence and Blow-upWe consider the Dirichlet problem for wave equations with p(x,t)- Laplacian and damping term. Under suitable condition on the data, we prove local and global existence theorems and study the finite time blow-up of the solutions. The analysis relies on the methods developed in :
[1.] Antontsev S.N., Díaz J.I., Shmarev S.I. Energy Methods for Free Boundary Problems: Applications to Non-linear PDEs and Fluid Mechanics. Bikhauser, Boston, 2002. Progress in Nonlinear Differential Equations and Their Applications, Vol. 48.
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