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

Date

2021-01-29

Authors

Antontsev, Stanislav
Ferreira, Jorge
Piskin, Erhan

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University, Department of Mathematics

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.

Description

Keywords

Global solution, Blow up, Petrovsky equation, Variable-exponent nonlinearities

Citation

Antontsev, S., Ferreira, J., & Piskin, E. (2021). Existence and blow up of solutions for a strongly damped Petrovsky equation with variable-exponent nonlinearities. <i>Electronic Journal of Differential Equations, 2021</i>(06), pp. 1-18.

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Attribution 4.0 International

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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