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Local existence and blow up of solutions to a Petrovsky equation with variable-exponent nonlinearities
  • Jorge Ferreira,
  • Erhan Pişkin
Jorge Ferreira
Federal Fluminense University - Volta Redonda Campus
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Erhan Pişkin
Dicle University
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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.