## Taiwanese Journal of Mathematics

### Long Time Behavior for a Wave Equation with Time Delay

#### Abstract

In this paper, we consider the wave equation with internal time delay and source terms$u_{tt}(x,t) - \triangle u(x,t) + \mu_1 u_t(x,t) + \mu_2 u_t(x,t-\tau) + f(x,u) = h(x)$in a bounded domain. By virtue of Galerkin method combined with the priori estimates, we prove the existence and uniqueness of global solution under initial-boundary data for the above equation. Moreover, under suitable conditions on the forcing term $f(x,u)$ and $\mu_1$, $\mu_2$, the existence of a compact global attractor is proved. Further, the asymptotic behavior and the decay property of global solution are discussed.

#### Article information

Source
Taiwanese J. Math., Volume 21, Number 1 (2017), 107-129.

Dates
First available in Project Euclid: 1 July 2017

https://projecteuclid.org/euclid.twjm/1498874559

Digital Object Identifier
doi:10.11650/tjm.21.2017.7246

Mathematical Reviews number (MathSciNet)
MR3613976

Zentralblatt MATH identifier
1361.35105

#### Citation

Liu, Gongwei; Yue, Hongyun; Zhang, Hongwei. Long Time Behavior for a Wave Equation with Time Delay. Taiwanese J. Math. 21 (2017), no. 1, 107--129. doi:10.11650/tjm.21.2017.7246. https://projecteuclid.org/euclid.twjm/1498874559

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