Local existence and blow up of solutions to a Petrovsky equation with variable-exponent nonlinearities

Abstract

In this paper, we consider a nonlinear plate (or beam) Petrovsky equation with strong damping and source terms with variable exponents. The exponents of nonlinearity _p_(⋅) and _q_(⋅) are given functions. By using the Banach contraction mapping principle the local existence of a weak solutions is established under suitable assumptions on the variable exponents _p_ and _p_. We also show a finite time blow up result for the solutions with negative initial energy.