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2013 ASYMPTOTIC BEHAVIOR FOR A VISCOELASTIC WAVE EQUATION WITH A DELAY TERM
Shun-Tang Wu
Taiwanese J. Math. 17(3): 765-784 (2013). DOI: 10.11650/tjm.17.2013.2517

Abstract

The following viscoelastic wave equation with a delay term in internal feedback: \begin{equation*} \left\vert u_{t}\right\vert ^{\rho }u_{tt}-\Delta u-\Delta u_{tt} + \int_{0}^{t} g(t-s) \Delta u(s) ds + \mu _{1} u_{t}(x,t) + \mu _{2} u_{t}(x,t-\tau ) = 0, \end{equation*} is considered in a bounded domain. Under appropriate conditions on $\mu_{1}$, $\mu_{2}$ and on the kernel $g$, we prove the local existence result by Faedo-Galerkin method and establish the decay result by suitable Lyapunov functionals.

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Shun-Tang Wu. "ASYMPTOTIC BEHAVIOR FOR A VISCOELASTIC WAVE EQUATION WITH A DELAY TERM." Taiwanese J. Math. 17 (3) 765 - 784, 2013. https://doi.org/10.11650/tjm.17.2013.2517

Information

Published: 2013
First available in Project Euclid: 10 July 2017

zbMATH: 1297.35044
MathSciNet: MR3072260
Digital Object Identifier: 10.11650/tjm.17.2013.2517

Subjects:
Primary: 35L05 , 35L15 , 35L70 , 93D15

Keywords: asymptotic behavior , Delay , general decay , global existence

Rights: Copyright © 2013 The Mathematical Society of the Republic of China

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