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. Electronic Journal of Differential Equations, 2021(06), pp. 1-18.
Rights
Attribution 4.0 International