Stanislav Antontsev, Jorge Ferreira, Erhan Piskin
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.
DOI: https://doi.org/10.58997/ejde.2021.06
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Stanislav Antontsev Lavrentyev Institute of Hydrodynamics of SB RAS Novosibirsk, Russia email: antontsevsn@mail.ru |
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Jorge Ferreira Federal Fluminense University - UFF - VCE Department of Exact Sciences, Av. dos Trabalhadores 420 Volta Redonda RJ, Brazil email: ferreirajorge2012@gmail.com |
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Erhan Piskin Dicle University Department of Mathematics 21280 Diyarbakir, Turkey email: episkin@dicle.edu.tr |
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