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

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

Journal

Electronic Journal of Differential Equations
ISSN: 1072-6691

Output data

Year: 2021, Volume: 2021, Number: 06, Pages: 1-18 Pages count : 18

Tags

BLOW UP, GLOBAL SOLUTION, PETROVSKY EQUATION, VARIABLE-EXPONENT NONLINEARITIES

Authors

Antontsev Stanislav Nikolaevich ^1,2 , Ferreira Jorge ³ , Piskin Erhan ⁴

Affiliations

1	Lavrentyev Institute of Hydrodynamics of SB RAS, Novosibirsk, Russia
2	University of Lisbon
3	Federal Fluminense University
4	Dicle University. Department of Mathematics

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.

Antontsev S.N. , Ferreira J. , Piskin E.
Existence and blow up of solutions for a strongly damped Petrovsky equation with variable-exponent nonlinearities
Electronic Journal of Differential Equations. 2021. V.2021. N06. P.1-18. РИНЦ OpenAlex

Published print:

Jan 29, 2021

Elibrary:	46742313
OpenAlex:	W3193449460

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