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

Electronic Journal of Differential Equations

article

Stanislav Antontsev¹  Jorge Ferreira²  Erhan Piskin³ 

[1] Lavrentyev Institute of Hydrodynamics of SB RAS Novosibirsk;Federal Fluminense University - UFF - VCE Department of Exact Sciences;Dicle University Department of Mathematics 21280 Diyarbakir

关键词: Global solution;    blow up;    Petrovsky equation;    variable-exponent nonlinearities.;   

DOI  :  10.58997/ejde.2021.06

学科分类：数学（综合）

来源: Texas State University

【 摘 要 】

In this article, we consider a nonlinear plate (or beam) Petrovskyequation with strong damping and source terms with variable exponents.By using the Banach contraction mapping principle we obtain localweak solutions, under suitable assumptions on the variable exponentsp(.) and q(.).Then we show that the solution is global if p(.) ≥ q(.).Also, we prove that a solution with negative initial energy andp(.)

【 授权许可】

CC BY