Electron. J. Differential Equations, Vol. 2021 (2021), No. 06, pp. 1-18.

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

Stanislav Antontsev, Jorge Ferreira, Erhan Piskin

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.

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Stanislav Antontsev
Lavrentyev Institute of Hydrodynamics of SB RAS
Novosibirsk, Russia
email: antontsevsn@mail.ru
Jorge Ferreira
Federal Fluminense University - UFF - VCE
Department of Exact Sciences, Av. dos Trabalhadores
420 Volta Redonda RJ, Brazil
email: ferreirajorge2012@gmail.com
Erhan Piskin
Dicle University
Department of Mathematics
21280 Diyarbakir, Turkey
email: episkin@dicle.edu.tr

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