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...
Riesz basis property of Timoshenko beams with boundary feedback control.
Rigidity for the hyperbolic Monge-Ampère equation
Some properties of nonlinear partial differential equations are naturally associated with the geometry of sets in the space of matrices. In this paper we consider the model case when the compact set is contained in the hyperboloid , where , the set of symmetric matrices. The hyperboloid is generated by two families of rank-one lines and related to the hyperbolic Monge-Ampère equation . For some compact subsets containing a rank-one connection, we show the rigidity property of by imposing...
Rigorous derivation of Korteweg-de Vries-type systems from a general class of nonlinear hyperbolic systems
Rigorous derivation of Korteweg-de Vries-type systems from a general class of nonlinear hyperbolic systems
In this paper, we study the long wave approximation for quasilinear symmetric hyperbolic systems. Using the technics developed by Joly-Métivier-Rauch for nonlinear geometrical optics, we prove that under suitable assumptions the long wave limit is described by KdV-type systems. The error estimate if the system is coupled appears to be better. We apply formally our technics to Euler equations with free surface and Euler-Poisson systems. This leads to new systems of KdV-type.
Rotationally invariant periodic solutions of semilinear wave equations.
Rothe time-discretization method applied to a quasilinear wave equation subject to integral conditions.