Existence and blow up of solutions for a strongly damped Petrovsky equation with variable-exponent nonlinearities

Abstract

In this article, we consider a nonlinear plate (or beam) Petrovsky equation with strong damping and source terms with variable exponents. By using the Banach contraction mapping principle we obtain local weak solutions, under suitable assumptions on the variable exponents p(.) and q(.). Then we show that the solution is global if p(.) ≥ q(.). Also, we prove that a solution with negative initial energy and p(.)<q(.) blows up in finite time.

Keywords

• global solution
• blow up
• petrovsky equation
• variable-exponent nonlinearities