Energy Decay for Thermoviscoelastic Systems

Yuming Qin () and Zhiyong Ma ()
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Yuming Qin: Donghua University, Department of Applied Mathematics
Zhiyong Ma: Shanghai Second Polytechnic University

Chapter Chapter 9 in Global Well-posedness and Asymptotic Behavior of the Solutions to Non-classical Thermo(visco)elastic Models, 2016, pp 165-185 from Springer

Abstract: Abstract In this chapter, we shall consider the following thermoviscoelastic problem $$\begin{aligned} \left\{ \begin{array}{ll} u_{tt}-\Delta {u}+g*\Delta u+\nabla \vartheta =0, &{}\quad (x,t)\in \Omega \times (0,+\infty ),\\ \vartheta _{tt}-\Delta \vartheta _{t}-\Delta \vartheta +\mathrm{div} u_{tt}=0,&{}\quad (x,t)\in \Omega \times (0,+\infty ),\\ \vartheta =0,&{}\quad (x,t)\in \partial \Omega \times (0,+\infty ),\\ u=0, &{}\quad (x,t)\in \Gamma _{0}\times (0,+\infty ),\\ \frac{\partial u}{\partial \nu }-g*\frac{\partial u}{\partial \nu }+H(u_{t})=0, &{}\quad (x,t)\in \Gamma _{1}\times (0,+\infty )\\ \end{array}\right. \end{aligned}$$ with the initial data $$\begin{aligned} u(x,0)=u_0(x),\quad u_{t}(x,0)=u_{1}(x),\quad \vartheta (x,0)=\vartheta _0(x),\quad \vartheta _t(x,0)=\vartheta _1(x),\quad x\in \Omega , \end{aligned}$$

Keywords: Thermoviscoelastic System; Energy Decay; Explicit Decay Rate; Thermoviscoelastic Plates; Zuazua (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-981-10-1714-8_9

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