Electronic Journal of Differential Equations, 
Vol. 2021 (2021), No. 06, pp. 1-18.

Title: Existence and blow up of solutions for a strongly damped 
       Petrovsky equation with variable-exponent nonlinearities
       
Authors: Stanislav Antontsev (Lavrentyev Inst. of Hydrodynamics, Novosibirsk, Russia)
         Jorge Ferreira (Federal Fluminense Univ., RJ, Brazil)
         Erhan Piskin (Dicle Univ., Diyarbakir, Turkey)

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.

Submitted May 20, 2020. Published January 29, 2021.
Math Subject Classifications: 35A01, 35B44, 35L55.
Key Words: Global solution; blow up; Petrovsky equation;
           variable-exponent nonlinearities.