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2 edition of Energy decay rate of wave equations with indefinite damping found in the catalog.

Energy decay rate of wave equations with indefinite damping

Ahmed Benaddi

Energy decay rate of wave equations with indefinite damping

by Ahmed Benaddi

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  • 19 Currently reading

Published by Institut de recherche mathématique avancée in Strasbourg .
Written in English


Edition Notes

Statementpar Ahmed Benddai and Bopeng Rao.
SeriesPreṕublication de l"institut de recheche mathématique avancée ;, 1999/49
ContributionsRao, Bopeng.
Classifications
LC ClassificationsMLCM 2002/02142 (Q)
The Physical Object
Pagination20 leaves ;
Number of Pages20
ID Numbers
Open LibraryOL3631148M
LC Control Number2002424542

The damped wave equationResolvent estimates and a priori boundsSmooth dampingRough damping Decay rates for the damped wave equation on the torus Matthieu L eautaud Universit e Denis Diderot Paris 7 Joint work with Nalini Anantharaman Operator semigroups meet complex analysis, harmonic analysis, and mathematical physics. Herrnhut June, 4.   We introduce a new model of the nonlocal wave equation with a logarithmic damping mechanism, which is rather weak as compared with frequently studied fractional damping cases. We consider the Cauchy problem for the new model in \(\mathbf{R}^{n}\) and study the asymptotic profile and optimal decay rates of solutions as \(t \rightarrow \infty.

Decay results for arbitrary growth of the frictional damping term have been given by Amroun and Benaissa motivated by the works done by Lasiecka and Tataru, Liu and Zuazua, and Martinez [26,27] for damped wave equations. They established an explicit formula for the energy decay rates that need not to be of exponential or polynomial types. The one-dimensional wave equation with damping of indefinite sign in a bounded interval with Dirichlet boundary conditions is considered. It is proved that solutions decay uniformly exponentially to zero provided the damping potential is in theBV-class, has positive average, is small enough and satisfies a finite number of further constraints guaranteeing that the derivative of the real part.

DAMPING AND ENERGY DISSIPATION n D n nu e (() 2π = (0) −ξω2π / ω n m D n m n mu e −ξω π + ω π + += (() 2))(0) 2 ()/ {XE "Algorithms for:Evaluation of Damping" }The ratio of these two equations is: m m n n m e r u u = −ξ = π ξ − + 1 2 2 () {XE "Damping:Decay Ratio" }Taking the natural logarithm of this decay ratio, rm, and rewriting produces the. Energy structure and asymptotic profile of the linearized system of thermo-elastic equation in lower space dimensions Kimura, Yuki and Ogawa, Takayoshi,, ; Global existence and decay rate of strong solution to incompressible Oldroyd type model equations Yuan, Baoquan and Liu, Yun, Rocky Mountain Journal of Mathematics, ; Lp-Lq estimates for damped wave equations and their .


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Energy decay rate of wave equations with indefinite damping by Ahmed Benaddi Download PDF EPUB FB2

Journal of Differential Equations() Energy Decay Rate of Wave Equations with Indefinite Damping Ahmed Benaddi and Bopeng Rao Institut de Recherche Mathe matique Avance e, Universite Louis Pasteur de Strasbourg, 7, Rue Rene -Descartes, Strasbourg Cedex, France E-mail: benaddirao   We consider the one-dimensional wave equation with an indefinite sign damping and a zero order potential term.

Using a shooting method, we establish the asymptotic expansion of eigenvalues and eigenvectors of the damped wave equation for a large class of by: Energy Decay Rate of Wave Equations with Indefinite Damping Article in Journal of Differential Equations (2) March with 36 Reads How we measure 'reads'.

We consider the one-dimensional wave equation with an indefinite sign damping and a zero order potential term. Using a shooting method, we establish the asymptotic expansion of eigenvalues and eigenvectors of the damped wave equation for a large class of coefficients.

In addition, if the damping coefficient is “more positive than negative,” we prove that the energy of system decays Cited by: Optimal energy decay rates for some wave equations with double damping terms. Evolution Equations & Control Theory,8 (4): doi: /eect [13] Dalibor Pražák. On the dimension of the attractor for the wave equation with nonlinear by: ~~ Last Version Energy Decay And Boundary Control For Distributed Parameter Systems With Viscoelastic Damping ~~ Uploaded By Lewis Carroll, energy decay and boundary control for distributed parameter systems with viscoelastic damping sep 02 posted by dr seuss media text id online pdf ebook epub library.

Although the literature on the decay (estimates) of the energy of the wave equation with locally distributed damping is quite impressive [2][3][4][5][6][7][8][9]11,12,[14][15][16][17][18][19][   By means of global Carleman-type estimate, we study the stabilization problem of the wave equations with potential and indefinite damping.

The energy decay rate of the system is given explicitly. Also, we obtain an upper bound estimate on the negative damping to guarantee the energy of the system decays exponentially.

In this paper, we analyze the longtime behavior of the wave equation with local Kelvin-Voigt Damping. Through introducing proper class symbol and pseudo-diff-calculus, we obtain a Carleman estimate, and then establish an estimate on the corresponding resolvent operator.

As a result, we show the logarithmic decay rate for energy of the system without any geometric assumption on the subdomain on. Explicit estimates of the decay rate ω are given in terms of a and the biggest eigenvalue of (∂ xx − b).

Second, we show the existence of a global, small, smooth solution of the corresponding nonlinear wave equation u tt − σ(u x) x + a(x)u t + b(x)u = 0, if, additionally, the negative part of a is small enough compared with ω.

Abstract. We study the asymptotic behavior of energy for wave equations with nonlinear damping g(ut) = |ut|m−1ut in Rn (n ≥ 3) as time t → ∞. The main result shows a polynomial decay rate of energy under the condition 1 decay rates were found.

Introduction. () Energy Decay Rate of Wave Equations with Indefinite Damping. Journal of Differential Equations() Exponential stabilization of timoshenko beam with. Energy decay rates for solutions of the wave equation with linear damping in exterior domain.

Evolution Equations & Control Theory,5 (1): doi: /eect [2] Yinbin Deng, Yi Li, Wei Shuai. Existence of solutions for a class of p-Laplacian type equation with critical growth and potential vanishing at infinity.

Exponential decay rate for a wave equation with Dirichlet boundary control @article{DengExponentialDR, title={Exponential decay rate for a wave equation with Dirichlet boundary control}, author={Chuanxian Deng and Yan Liu and Weisheng Jiang and Falun Huang}, journal={Appl.

Math. Lett.}, year={}, volume={20}, pages={} }. Ikehata and T. Komatsu, Fast energy decay for wave equations with variable damping coefficients in the 1-D half line, Differential and Integral Equations 29(5–6) (), – [9] R. Ikehata and T. Matsuyama, L 2 -behaviour of solutions to the linear heat and wave equations in exterior domains, Sci.

Math. Japon. 55 (), 33– DOI: /JMSJ/ Corpus ID: Optimal decay rate of the energy for wave equations with critical potential @article{IkehataOptimalDR, title={Optimal decay rate of the energy for wave equations with critical potential}, author={Ryo Ikehata and Grozdena Todorova and Borislav Yordanov}, journal={Journal of The Mathematical Society of Japan}, year={}, volume={65}, pages.

Using the multiplier method and a special integral inequality we obtain sharp energy decay rate estimates for the wave equation in the presence of nonlinear distributed or boundary feedbacks.

For simplicity we restrict ourselves to the wave equation, but. Abstract. Under appropriate assumptions the energy of wave equations with damping and variable coefficients c(x)utt − div(b(x)∇u) + a(x)ut = h(x) has been shown to decay.

Determining the rate of decay for the higher order energies involving the kth order spatial and time derivatives has been an open. Obtain the sharp gain of decay rates for the L2 norms of the higher order spatial derivatives.

Regarding the first problem, Nakao [11] uses the decay of the damping to find decay rates for the first and second order energies when c(x) = b(x) = 1, and h(x,t) = 0. He shows that the energy has the following decay rate E(t;u):= 1 2. “ A general method for proving sharp energy decay rates for memory-dissipative evolution equations J.

A., “ Exponential decay for the solution of semilinear viscoelastic wave equations with localized damping,” Electron. “ On the decay of the energy for systems with memory and indefinite.

By means of global Carleman-type estimate, we study the stabilization problem of the wave equations with potential and indefinite damping. The energy decay rate of the system is given explicitly. Also, we obtain an upper bound estimate on the negative damping to guarantee the energy .Abstract. We consider the wave equation damped with a boundary nonlinear velocity feedback (u0).

Under some geometrical conditions, we prove that the energy of the system decays to zero with an explicit decay rate estimate even if the function has not a polynomial behavior in zero. S. Berrimi and S. A. Messaoudi, “ Exponential decay of solutions to a viscoelastic equation with nonlinear localized damping,” Electron J.

Differ. Equati 1– 10 (). Google Scholar; 9. M. M. Cavalcanti and H. P. Oquendo, “ Frictional versus viscoelastic damping in a semilinear wave equation,” SIAM J. Control Optim.

42,