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polynomial decay and Blow Up of Solutions for Variable Coefficients Viscoelastic Wave Equation with Acoustic Boundary Conditions

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Acta Mathematica Sinica,English Series 2016年第2期32卷 153-174页

作者： Yamna BOUKHATEM Benyattou BENABDERRAHMANE Laboratory of Computer Sciences and Mathematics Faculty of SciencesUniversity of LaghouatP.O.BOX 37GLaghouat(03000)Algeria Faculty of Mathematics and Computer Sciences University of M'SilaAlgeria

A variable coefficient viscoelastic wave equation with acoustic boundary conditions and nonlinear source term is considered. Under suitable conditions on the initial data and the relaxation function g, we show the polynomial decay of the energy solution and the blow up of solutions by energy methods. The estimates for the lifespan of solutions are also given.

关键词： Acoustic boundary conditions blow up polynomial decay variable coefficients viscoelas-tic wave equation

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GLOBAL EXISTENCE, UNIFORM decay AND EXPONENTIAL GROWTH FOR A CLASS OF SEMI-LINEAR WAVE EQUATION WITH STRONG DAMPING

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Acta Mathematica Scientia 2013年第1期33卷 41-58页

作者：陈化刘功伟 School of Mathematics and Statistics Wuhan University

In this paper, we consider the nonlinearly damped semi-linear wave equation associated with initial and Dirichlet boundary conditions. We prove the existence of a local weak solution and introduce a family of potential wells and discuss the invariants and vacuum isolating behavior of solutions. Furthermore, we prove the global existence of solutions in both cases which are polynomial and exponential decay in the energy space respectively, and the asymptotic behavior of solutions for the cases of potential well family with 0 〈 E（0）〈 d. At last we show that the energy will grow up as an exponential function as time goes to infinity, provided the initial data is large enough or E（0）〈 0.

关键词： strong damping nonlinear damping global existence polynomial decay exponential decay exponential growth

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Asymptotic Behavior of a Bi-Dimensional Hybrid System

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Applied Mathematics 2015年第8期6卷 1228-1234页

作者： Pedro Gamboa Jaime E.Munoz Octavio Vera Margareth Alves Departamento de Matemática Instituto de MatemáticasUniversidade Federal do Rio de JaneiroRio de JaneiroBrazil Laboratorio Nacional de Computacao Científica PetrópolisBrazil Departamento de Matemática Facultad de CienciasUniversidad del Bo-BoConcepciónChile Departamento de Matemática UFVVicosaBrazil

We study the asymptotic behavior of the solutions of a Hybrid System wrapping an elliptic operator.

关键词： Hybrid System Compressible Stabilization Asymptotic Behavior decay Rate Generator Infinitesimal polynomial decay

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Stability and Control on a Model in Fluid-Structure Interaction

Stability and Control on a Model in Fluid-Structure Interact...

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第二十二届中国控制会议

作者： Enrique Zuazua Departamento de Matemáticas Facultad de CienciasUniversidad Autónoma de MadridMadridSpain28049

＜正＞We consider a linearized and simplified model for fluid-structure interaction. The domain where the system evolves consists in two parts in which the wave and heat equations are satisfied respectively, with transmission conditions at the interface. First of all, based on a compact decoupling technique, we show that the solutions of the system do not decay exponentially. Next, by means of a careful spectral asymptotic analysis on high frequencies, we obtain the sharp polynomial decay rate of smooth solutions. Then, by combining sidewise energy estimates for the wave equation and Carleman inequalities for the heat one, we show the observability/null -controllability of the system with observation/control through the wave component. Finally, we prove the null-controllability of the system when the control acts on the boundary where the heat equation holds. The proof is based on a new Inghamtype inequality, which follows from the spectral analysis we develop and the observability inequality we get in the case that the observation is made through the wave component.

关键词： Fluid-structure interaction coupled heat-wave system compact decoupling technique polynomial decay boundary control and observability

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