Well-posedness and exponential stability for a plate equation with time-varying delay and past history

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Well-posedness and exponential stability for a plate equation with time-varying delay and past history

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作者：Baowei Feng
关键词：Plate equation ; Viscoelasticity ; Memory ; Delay ; Energy decay
刊名：Zeitschrift für angewandte Mathematik und Physik
出版年：2017
出版时间：February 2017
年：2017
卷：68
期：1
全文大小：
刊物主题：Theoretical and Applied Mechanics; Mathematical Methods in Physics;
出版者：Springer International Publishing
ISSN：1420-9039
卷排序：68

文摘

This paper is concerned with a class of plate equation with past history and time-varying delay in the internal feedback $$\begin{aligned} u_{tt}+\alpha \Delta ^2 u-\int \limits ^t_{-\infty }g(t-s)\Delta ^2 u(s)\mathrm{d}s+\mu _1u_t+\mu _2u_t(t-\tau (t))+f(u)=h(x), \end{aligned}$$defined in a bounded domain of ${\mathbb {R}}^n$$(n\ge 1)$ with some suitable initial data and boundary conditions. For arbitrary real numbers $\mu _1$ and $\mu _2$, we proved the global well-posedness of the problem. Results on stability of energy are also proved under some restrictions on $\mu _1$, $\mu _2$ and $h(x)=0$.KeywordsPlate equationViscoelasticityMemoryDelayEnergy decayMathematics Subject Classification35L3574Dxx93D1593D20References1.Alabau-Boussouira F., Nicaise S., Pignotti C.: Exponential stability of the wave equation with memory and time delay. In: New prospects in direct, inverse and control problems for evolution equations. INdAM Series, Vol. 10, pp. 1–22. 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Phys. 51, 032701 (2010)MathSciNetCrossRefMATHGoogle ScholarCopyright information© Springer International Publishing 2016Authors and AffiliationsBaowei Feng1Email author1.Faculty of Economic MathematicsSouthwestern University of Finance and EconomicsChengduPeople’s Republic of China About this article CrossMark Publisher Name Springer International Publishing Print ISSN 0044-2275 Online ISSN 1420-9039 About this journal Reprints and Permissions Article actions .buybox { margin: 16px 0 0; position: relative; } .buybox { font-family: Source Sans Pro, Helvetica, Arial, sans-serif; font-size: 14px; font-size: .875rem; } .buybox { zoom: 1; } .buybox:after, .buybox:before { content: ''; display: table; } .buybox:after { clear: both; } /*---------------------------------*/ .buybox .buybox__header { border: 1px solid #b3b3b3; border-bottom: 0; padding: 8px 12px; position: relative; background-color: #f2f2f2; } .buybox__header .buybox__login { font-family: Source Sans Pro, Helvetica, Arial, sans-serif; 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