... [1] N. Anantharaman and M. L´eautaud. Sharp polynomial decay rates for the damped **wave** **equation** on the torus. Anal. PDE, 7(1):159–214, 2014. With an appendix by St´ephane Nonnenmacher. [2] C. Bardos, G. ...

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... properties of (1) have been obtained by various authors. For instance, in a very general context, Lebeau related the geometry of the undamped geodesics, the spectral asymptotics of the τ n and the energy decay of the ...

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... free **wave** **equation** ...damped **wave** **equation** in an unbounded manifold and with a non-linearity, but assuming that the damping satisfies γ(x) ≥ α > 0 outside a compact set, see [33], [10], [9] ...

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... [4] Rhouma Mlayeh, Samir Toumi, and Lotfi Beji. Backstepping boundary observer based-control for hyperbolic PDE in rotary drilling system. Applied Mathematics and Computation, 322:66–78, 2018. [5] Christophe Prieur, ...

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... Helmholtz **equation** with a limited memory imprint in the high frequency regime, and (2) inverting, or precondi- tioning the **wave**-**equation** Hessian in order to perform high- quality Gauss-Newton ...

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... isotropic **wave** speed (in this note), or other parameters such as elastic moduli and density; and the (nonlinear) forward modeling op- erator F results from simulating **wave** equations forward in time and ...

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... Received: date / Accepted: date Abstract A minimum effort optimal control problem for the undamped **wave** **equation** is considered which involves L ∞ –control costs. Since the problem is non-differentiable a ...

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... Abstract We prove error estimates for the **wave** **equation** semi-discretized in space by the hybrid high-order (HHO) method. These estimates lead to optimal convergence rates for smooth solutions. We consider ...

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... [2] Katrin Boxberger. Propagation d’ ondes dans un réseau de fentes minces: Étude math- ématique et simulation. Master’s thesis, Université Paris-Sud, 2009. [3] Gary Cohen, Patrick Joly, and Nathalie Tordjman. ...

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... discrete **wave** **equation** with a weak stochastic ...Uhlenbeck **equation** for the limit **wave** function that holds both for square integrable and statistically homogeneous initial ...

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... Adjacently, this discussion raises the problem of discussing the numerical efficiency of vari- ous control design approaches. It would be interesting to compare our approach, developed in the present paper, with other ...

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... . The proof of Theorem 1.1 we present here follows the method initiated by the first and second authors in [2]. This method is mainly based on a spectral decomposition combined with an observability inequality. Due to ...

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... [12] P. Jounieaux, Y. Privat, E. Tr´ elat, Optimal boundary observation domain for the **wave** **equation**, ongoing work. [13] C. Morawetz, Notes on time decay and scatteringfor some hyperbolic problems, Regional ...

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... ) satisfying V (x) = O hxi −(n+1)/2−ǫ , ǫ > 0. 1 Introduction and statement of results High frequency dispersive estimates with loss of (n − 3)/2 have been recently proved in [9] for the **wave** **equation** ...

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... 1. Introduction One of the standard questions in geometric control theory concerns the so-called sta- bilization problem: given a dissipative **wave** **equation** on a manifold, one is interested in the behaviour ...

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... For **wave** propagation in higher dimensions, we do not have access to this kind of information, and do not know how to separate scales for density and elastic constants, in order to proceed to an homogenization of ...

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... 1. Introduction. The design of accurate absorbing boundary conditions (ABCs) for the numerical calculation of waves in the time domain is already an old subject since the major work of Engquist and Majda [11], [12] in ...

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... PIECEWISE SMOOTH DAMPING NICOLAS BURQ AND CHENMIN SUN Abstract. We study the energy decay rate of the Kelvin-Voigt damped **wave** **equation** with piecewise smooth damping on the multi-dimensional domain. Under ...

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... 0. Introduction The Webster–Lokshin system is a dissipative model that describes acoustic waves traveling in a duct with visco-thermal losses at the lateral walls. This system couples a **wave** **equation** with ...

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... archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la ...

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