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2013 GENERAL DECAY RATE ESTIMATE FOR THE ENERGY OF A WEAK VISCOELASTIC EQUATION WITH AN INTERNAL TIME-VARYING DELAY TERM
Wenjun Liu
Taiwanese J. Math. 17(6): 2101-2115 (2013). DOI: 10.11650/tjm.17.2013.2968

Abstract

In this paper we consider the weak viscoelastic equation with an internal time-varying delay term $$u_{tt}(x,t)-\Delta u(x,t)+\alpha(t)\int_{0}^{t}g(t-s)\Delta u(x,s)\, {\rm d}s +a_{0}u_{t}(x,t)+a_{1}u_{t}(x,t-\tau(t))=0$$ in a bounded domain. By introducing suitable energy and Lyapunov functionals, under suitable assumptions, we establish a general decay rate estimate for the energy, which depends on the behavior of both $\alpha$ and $g$.

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Wenjun Liu. "GENERAL DECAY RATE ESTIMATE FOR THE ENERGY OF A WEAK VISCOELASTIC EQUATION WITH AN INTERNAL TIME-VARYING DELAY TERM." Taiwanese J. Math. 17 (6) 2101 - 2115, 2013. https://doi.org/10.11650/tjm.17.2013.2968

Information

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

zbMATH: 1286.35040
MathSciNet: MR3141876
Digital Object Identifier: 10.11650/tjm.17.2013.2968

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

Keywords: general decay rate , internal feedback , time-varying delay , weak viscoelastic equation

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

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Vol.17 • No. 6 • 2013
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