Propagation des ondes dans les variétés à coins
Propagation des singularités au bord d’ouverts de
Propagation des singularités le long de courbes microbicaractéristiques pour des opérateurs pseudodifférentiels à caractéristiques doubles. I
Propagation des singularités pour les équations aux dérivées partielles non linéaires
Propagation des singularités pour les équations des ondes semi-linéaires
Propagation d'oscillations près d'un point diffractif
Propagation et réflexion des singularités pour l'équation de Schrödinger non linéaire
Nous construisons un calcul paradifférentiel adapté à l'équation de Schrödinger qui nous permet de montrer un théorème de propagation des singularités pour l'équation de Schrödinger non linéaire en adaptant la méthode de Bony. Nous construisons également la version tangentielle du calcul précédent qui nous permet de montrer un théorème de réflexion transverse des singularités pour l'équation de Schrödinger non linéaire. Nous utilisons alors ce théorème pour calculer l'opérateur...
Propagation of analytic singularities for the Schrödinger Equation
Propagation of analyticity of solutions to the Cauchy problem for Kirchhoff type equations
We shall give the local in time existence of the solutions in Gevrey classes to the Cauchy problem for Kirhhoff equations of -laplacian type and investigate the propagation of analyticity of solutions for real analytic deta. When , his equation as the global real analytic solution for the real analytic initial data.
Propagation of singularities and local solvability in Gevrey classes
Propagation of singularities and maximal functions in the plane.
Propagation of singularities for a first order semi-linear system in
Propagation of singularities for the wave equation on manifolds with corners
In this talk we describe the propagation of and Sobolev singularities for the wave equation on manifolds with corners equipped with a Riemannian metric . That is, for , , and solving with homogeneous Dirichlet or Neumann boundary conditions, we show that is a union of maximally extended generalized broken bicharacteristics. This result is a counterpart of Lebeau’s results for the propagation of analytic singularities on real analytic manifolds with appropriately stratified boundary,...
Propagation of singularities in many-body scattering in the presence of bound states
In these lecture notes we describe the propagation of singularities of tempered distributional solutions of , where is a many-body hamiltonian , , , and is not a threshold of , under the assumption that the inter-particle (e.g. two-body) interactions are real-valued polyhomogeneous symbols of order (e.g. Coulomb-type with the singularity at the origin removed). Here the term “singularity” provides a microlocal description of the lack of decay at infinity. Our result is then that the...
Propagation of uniform Gevrey regularity of solutions to evolution equations
We investigate the propagation of the uniform spatial Gevrey , σ ≥ 1, regularity for t → +∞ of solutions to evolution equations like generalizations of the Euler equation and the semilinear Schrödinger equation with polynomial nonlinearities. The proofs are based on direct iterative arguments and nonlinear Gevrey estimates.
Propagation of weak discontinuities for quasilinear hyperbolic systems with coefficients functionally dependent on solutions
The propagation of weak discontinuities for quasilinear systems with coefficients functionally dependent on the solution is studied. We demonstrate that, similarly to the case of usual quasilinear systems, the transport equation for the intensity of weak discontinuity is quadratic in this intensity. However, the contribution from the (nonlocal) functional dependence appears to be in principle linear in the jump intensity (with some exceptions). For illustration, several examples, including two hyperbolic...
Propagation, reflection and refraction of singularities for a hyperbolic transmission problem in two adjacent angular regions
Properties of a quasi-uniformly monotone operator and its application to the electromagnetic $p$-$\text {curl}$ systems
In this paper we propose a new concept of quasi-uniform monotonicity weaker than the uniform monotonicity which has been developed in the study of nonlinear operator equation $Au=b$. We prove that if $A$ is a quasi-uniformly monotone and hemi-continuous operator, then $A^{-1}$ is strictly monotone, bounded and continuous, and thus the Galerkin approximations converge. Also we show an application of a quasi-uniformly monotone and hemi-continuous operator to the proof of the well-posedness and convergence...
Properties of some integrals related to partial differential equations of order higher than two
We construct fundamental solutions of some partial differential equations of order higher than two and examine properties of these solutions and of some related integrals. The results will be used in our next paper concerning boundary-value problems for these equations.
Proximité évanescente. II. Équations fonctionnelles pour plusieurs fonctions analytiques