wave equation
CONCENTRATION OF LAPLACE EIGENFUNCTIONS AND STABILIZATION OF WEAKLY DAMPED WAVE EQUATION
... [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. ...
25
EIGENMODES OF THE DAMPED WAVE EQUATION AND SMALL HYPERBOLIC SUBSETS
... 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 ...
25
Exponential decay for the damped wave equation in unbounded domains
... 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] ...
26
Control of a Wave Equation with a Dynamic Boundary Condition
... [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, ...
7
Approximate inversion of the wave-equation Hessian via randomized matrix probing
... 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 ...
5
Approximate inversion of the wave-equation Hessian via randomized matrix probing
... 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 ...
6
A minimum effort optimal control problem for the wave equation.
... 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 ...
30
Convergence analysis of hybrid high-order methods for the wave equation
... 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 ...
32
Numerical resolution of the wave equation on a network of slots
... [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. ...
36
Asymptotics of the solutions of the stochastic lattice wave equation
... discrete wave equation with a weak stochastic ...Uhlenbeck equation for the limit wave function that holds both for square integrable and statistically homogeneous initial ...
31
PI regulation control of a 1-D semilinear wave equation
... 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 ...
31
Determining the potential in a wave equation without a geometric condition. Extension to the heat equation
... . 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 ...
11
Optimal design of boundary observers for the wave equation
... [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 ...
11
Low frequency dispersive estimates for the wave equation in higher dimensions
... ) 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 ...
11
Energy decay for the damped wave equation under a pressure condition
... 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 ...
33
2-D non-periodic homogenization of the elastic wave equation: SH case
... 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 ...
39
AN ANALYSIS OF HIGHER ORDER BOUNDARY CONDITIONS FOR THE WAVE EQUATION
... 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 ...
30
DECAY FOR THE KELVIN-VOIGT DAMPED WAVE EQUATION: PIECEWISE SMOOTH DAMPING
... 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 ...
34
Efficient solution of a wave equation with fractional-order dissipative terms
... 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 ...
9
LAPLACE EIGENFUNCTIONS AND DAMPED WAVE EQUATION II: PRODUCT MANIFOLDS
... 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 ...
11