记忆热-梁方程传输系统的指数稳定性
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摘要
本文研究的是由记忆热方程和Euler-Bernoulli梁方程构成的传输系统,其中热方程作为梁方程的控制器.通过频域上的能量乘子法,我们建立了耦合系统的指数稳定性.
An Euler-Bernoulli beam equation connected with a heat equation with memory through boundary weak connection is concerned, where the heat equation is considered a controller for beam equation. By energy multiplier method in frequency domain, we establish exponential stability for coupled system.
An Euler-Bernoulli beam equation connected with a heat equation with memory through boundary weak connection is concerned, where the heat equation is considered a controller for beam equation. By energy multiplier method in frequency domain, we establish exponential stability for coupled system.
引文
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[2]Pandolfi L.The controllability of the Gurtin-Pipkin equation:A cosine operator approach(J).Appl Math Optim,2005,52:143-165.
[3]Wang J M,Miroslav K.Stability of an interconnected system of Euler-bernoulli beam and heat equation with boundary coupling[J].ESAIM:COCV,2015,21:1029-1052.
[4]Zhang Q,Guo B Z,Wang J M.Stabilization of the Euler-Bernoulli equation via boundary connection with heat Equation[J].Math Control Signals Systems,2014,26:77-118.
[5]Zhang Q.Stability analysis of an interactive system of wave equation and heat equation with memory[J].Z Angew Math Phys,2014,65:905-923.
[6]Huang F.Characteristic conditions for exponential stability of linear dynamical systems in Hilbert spaces[J].Annals of Differential Equations,1985,1:43-56.
[7]Pazy A.Semigroup of linear operators and applications to partial differential equations[M].New York:Springer-Verlag,1983.
[8]Prüss J.On the spectrum of C_0-semigroups[J].Trans Am Math Soc,1984,284:847-857.
[9]Zhang Q,Huang F.Boundary stabilization for a hybrid system of viscoelasticity[J].SIAM J Control Optim,2003,42:1643-1660.
[10]Curtain R F,Zwart H J.An introduction to infinite-dimensional linear system theory[M].New York:Springer,1995.