Decay Estimate for the Time-Delayed Fourth-Order Wave Equations

Authors : Müge MEYVACI

Pages : 142-150

Doi:10.36753/mathenot.777927

View : 31 | Download : 10

Publication Date : 2021-09-30

Article Type : Research Paper

Abstract :The objective of this article is to analyze the stability of solutions for the following fourth- order nonlinear wave equations with an internal delay term: \begin{equation*} u_{tt} + \Delta^2 u + u + \sigma_1insert ignore into journalissuearticles values(t); |u_{t}insert ignore into journalissuearticles values(x,t);|^{2m-2} u_tinsert ignore into journalissuearticles values(x,t); + \sigma_2insert ignore into journalissuearticles values(t); |u_{t} insert ignore into journalissuearticles values(x,t-\tau);|^{2m-2} u_tinsert ignore into journalissuearticles values(x,t-\tau); = 0. \end{equation*} We obtain appropriate conditions on $\sigma_1insert ignore into journalissuearticles values(t);$ and $\sigma_2insert ignore into journalissuearticles values(t);$ for the decay properties of the solutions. The multiplier technique and nonlinear integral inequalities are used in the proof.
Keywords : fourth order wave, asymptotic behavior, energy decay rate

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