Reflectionless boundary propagation formulas for partial wave solutions to the wave equation.
Régularité de la solution d'un problème de Cauchy fortement non linéaire à données singulières en un point
Dans cet article, on étudie la régularité d’une solution réelle, appartenant à pour assez grand, d’une équation aux dérivées partielles strictement hyperbolique et fortement non linéaire d’ordre deux. On suppose que les données de Cauchy sur une hypersurface spatiale lisse sont régulières en dehors d’un point, et ont une singularité conormale en ce point; on démontre alors que la réunion des bicaractéristiques nulles issues de ce point est, en dehors de ce point, une hypersurface lisse et...
Regularity of the solutions of second order evolution equations and their attractors
Regularity results for semilinear and geometric wave equations
Regularization and finite element approximation of the wave equation with Dirichlet boundary data
Relation de Poisson pour l'équation des ondes dans un ouvert non borné
Remark on the null-condition for the nonlinear wave equation
Dimostriamo l'esistenza della soluzione globale per un sistema di equazioni delle onde con nonlinearità quadratica dipendente dalle variabili spazio-tempo. Come in [3] la tecnica è basata sulla trasformazione di Penrose.
Remarks on Carleman estimates and exact controllability of the Lamé system
In this paper we established the Carleman estimate for the two dimensional Lamé system with the zero Dirichlet boundary conditions. Using this estimate we proved the exact controllability result for the Lamé system with with a control locally distributed over a subdomain which satisfies to a certain type of nontrapping conditions.
Remarques sur le problème de Cauchy pour l'équation des ondes
Representation theorem for the solution of weakly hyperbolic equations with fast oscillating coefficients
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.