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The energy in a square membrane Ω subject to constant viscous damping on a subset $ω \subset Ω$ decays exponentially in time as soon as ω satisfies a geometrical condition known as the “Bardos-Lebeau-Rauch” condition. The rate $τ (ω)$ of this decay satisfies $τ (ω) = 2 min (- μ (ω), g (ω))$ (see Lebeau [Math. Phys. Stud.19 (1996) 73–109]). Here $μ (ω)$ denotes the spectral abscissa of the damped wave equation operator and $g (ω)$ is a number called the geometrical quantity of ω and defined as follows. A ray in Ω is the trajectory generated by the free motion...

The Leading Singularity of Scattering Kernel for a Transparent Obstacle.

Sönke Hansen (1987/1988)

Mathematische Annalen

The light in the neighborhood of a caustic

J. J. Duistermaat (1976/1977)

Séminaire Bourbaki

The linear symmetric systems associated with the modified Cherednik operators and applications

Hatem Mejjaoli (2012)

Annales mathématiques Blaise Pascal

We introduce and study the linear symmetric systems associated with the modified Cherednik operators. We prove the well-posedness results for the Cauchy problem for these systems. Eventually we describe the finite propagation speed property of it.

The null condition and global existence of nonlinear elsastic waves.

Thomas C. Sideris (1996)

Inventiones mathematicae

The propagation of singularities for pseudo-differential operators with self-tangential characteristics

N. Dencker (1987/1988)

Séminaire Équations aux dérivées partielles (Polytechnique)

The radiation field is a Fourier integral operator

Antônio Sá Barreto, Jared Wunsch (2005)

Annales de l’institut Fourier

We show that the ``radiation field'' introduced by F.G. Friedlander, mapping Cauchy data for the wave equation to the rescaled asymptotic behavior of the wave, is a Fourier integral operator on any non-trapping asymptotically hyperbolic or asymptotically conic manifold. The underlying canonical relation is associated to a ``sojourn time'' or ``Busemann function'' for geodesics. As a consequence we obtain some information about the high frequency behavior of the scattering...

The relationship between the local temperature and the local heat flux within a one-dimensional semi-infinite domain of heat wave propagation.

Kulish, Vladimir V., Novozhilov, Vasily B. (2003)

Mathematical Problems in Engineering

The second-order Klein-Gordon field equation.

Gomes, D., Capelas de Oliveira, E. (2004)

International Journal of Mathematics and Mathematical Sciences

The two-dimensional eikonal equation.

Borovskikh, A.V. (2006)

Sibirskij Matematicheskij Zhurnal

The uniform exponential stability and the uniform stability at constantly acting disturbances of a periodic solution of a wave equation

Jiří Neustupa (1976)

Czechoslovak Mathematical Journal

We prove an observability estimate for a wave equation with rapidly oscillating density, in a bounded domain with Dirichlet boundary condition.

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Temps de vie et comportement explosif des solutions d'équations d'ondes quasi-linéaires en dimension deux. I

The behaviour of the Gaussian beam in an anisotropic medium with an interface between two media.

The Cauchy problem for non linear wave equations in domains with moving boundary

The Cauchy problem for nonlinear wave equations in the homogeneous Sobolev space

The exponential stability of a coupled hyperbolic/parabolic system arising in structural acoustics.

The fictitious domain method for the mixed finite element approximation of the wave equation

The geometrical quantity in damped wave equations on a square