Well-Posedness and Blow-Up of Solutions for a Variable Exponent Nonlinear Petrovsky Equation

In this article, we investigate a nonlinear Petrovsky equation with variable exponent and damping terms. First, we establish the local existence using the Faedo-Galerkin approximation method under the conditions of positive initial energy and appropriate constraints on the variable exponents p & sdot; and q & sdot;. Finally, we prove a finite-time blow-up result for negative initial energy.

Keyword: global existence; wave-equation