Polynomial-exponential stability and blow-up solutions to a nonlinear damped viscoelastic Petrovsky equation

被引：0
作者：
Peyravi A. [1 ]
Tahamtani F. [1 ]
机构：
[1] Department of Mathematics, College of Sciences, Shiraz University, Shiraz
来源：
SeMA Journal | 2020年 / 77卷 / 2期
关键词：
Blow-up; Stability; Viscoelastic Petrovsky equation;
D O I：
10.1007/s40324-019-00210-0
中图分类号：
学科分类号：
摘要：
This work is concerned with the initial boundary value problem for a nonlinear viscoelastic Petrovsky equation utt+Δ2u-∫0tg(t-τ)Δ2u(τ)dτ-Δut-Δutt+ut|ut|m-1=u|u|p-1.We prove that the solution energy has polynomial rate of decay, even if the kernel g decays exponentially provided m> 1 while decay rates is exponentially in the case of weak damping. The unbounded properties of solutions in two cases m= 1 and p> m≥ 1 have been also investigated. For the first case, we prove the blow-up of solutions with different ranges of initial energy. For the second case, we prove blow-up of solutions under some restrictions on g when the initial energy is negative or non negative at less than potential well depth. © 2019, Sociedad Española de Matemática Aplicada.
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页码：181 / 201
页数：20
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