Remarks on vacuum state and uniqueness of concentration process.
Remarks on weak stabilization of semilinear wave equations
If a second order semilinear conservative equation with esssentially oscillatory solutions such as the wave equation is perturbed by a possibly non monotone damping term which is effective in a non negligible sub-region for at least one sign of the velocity, all solutions of the perturbed system converge weakly to 0 as time tends to infinity. We present here a simple and natural method of proof of this kind of property, implying as a consequence some recent very general results of Judith Vancostenoble....
Remarks on weak stabilization of semilinear wave equations
If a second order semilinear conservative equation with esssentially oscillatory solutions such as the wave equation is perturbed by a possibly non monotone damping term which is effective in a non negligible sub-region for at least one sign of the velocity, all solutions of the perturbed system converge weakly to 0 as time tends to infinity. We present here a simple and natural method of proof of this kind of property, implying as a consequence some recent very general results of Judith Vancostenoble. ...
Remarque sur «R. G. McLenaghan : on the validity of Huygens principle for second order partial differential equations with four independent variables. I»
Remarques sur la caractérisation des problèmes mixtes bien posés pour un opérateur hyperbolique
Remarques sur la formulation cinétique des lois de conservation scalaires
Remarques sur le problème de Cauchy pour l'équation des ondes
Remarques sur les systèmes fortement hyperboliques
Remarques sur l'optique géométrique non linéaire multidimensionnelle
Removability of the wave singularities in the plane.
Removability of the wave singularities in the plane. (Summary).
Renormalized entropy solutions of scalar conservation laws
Representation theorem for the solution of weakly hyperbolic equations with fast oscillating coefficients
Resolución del problema de Cauchy para ecuaciones en derivadas parciales totalmente hiperbólicas.
Résolution de l’équation où est linéaire et dérive d’un potentiel convexe
Resolution of the Cauchy problem for several hyperbolic systems arising in chemical engineering
Resolvent estimates and the decay of the solution to the wave equation with potential
We prove a weighted estimate for the solution to the linear wave equation with a smooth positive time independent potential. The proof is based on application of generalized Fourier transform for the perturbed Laplace operator and a finite dependence domain argument. We apply this estimate to prove the existence of global small data solution to supercritical semilinear wave equations with potential.
Resolvent estimates for scalar fields with electromagnetic perturbation.
Resolvent estimates in controllability theory and applications to the discrete wave equation
We briefly present the difficulties arising when dealing with the controllability of the discrete wave equation, which are, roughly speaking, created by high-frequency spurious waves which do not travel. It is by now well-understood that such spurious waves can be dealt with by applying some convenient filtering technique. However, the scale of frequency in which we can guarantee that none of these non-traveling waves appears is still unknown in general. Though, using Hautus tests, which read the...
Resonances for transparent obstacles
This paper is concerned with the distribution of the resonances near the real axis for the transmission problem for a strictly convex bounded obstacle in , , with a smooth boundary. We consider two distinct cases. If the speed of propagation in the interior of the body is strictly less than that in the exterior, we obtain an infinite sequence of resonances tending rapidly to the real axis. These resonances are associated with a quasimode for the transmission problem the frequency support of...