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
The energy in a square membrane Ω subject to constant viscous damping on a subset decays exponentially in time as soon as ω satisfies a geometrical condition known as the “Bardos-Lebeau-Rauch” condition. The rate of this decay satisfies (see Lebeau [Math. Phys. Stud.19 (1996) 73–109]). Here denotes the spectral abscissa of the damped wave equation operator and 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.
The light in the neighborhood of a caustic
The linear symmetric systems associated with the modified Cherednik operators and applications
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.
The propagation of singularities for pseudo-differential operators with self-tangential characteristics
The radiation field is a Fourier integral operator
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.
The second-order Klein-Gordon field equation.
The two-dimensional eikonal equation.
The uniform exponential stability and the uniform stability at constantly acting disturbances of a periodic solution of a wave equation
The wave equation with oscillating density : observability at low frequency
The wave equation with oscillating density : observability at low frequency
The wave equation with oscillating density: observability at low frequency
We prove an observability estimate for a wave equation with rapidly oscillating density, in a bounded domain with Dirichlet boundary condition.