Propagation of singularities for a first order semi-linear system in
Propagation of singularities for interior mixed hyperbolic problem
Propagation of singularities for linear partial differential equations and reflections at a boundary
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 waves in a randomly stratified medium: an inverse problem.
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
Propagation through trapped sets and semiclassical resolvent estimates
Motivated by the study of resolvent estimates in the presence of trapping, we prove a semiclassical propagation theorem in a neighborhood of a compact invariant subset of the bicharacteristic flow which is isolated in a suitable sense. Examples include a global trapped set and a single isolated periodic trajectory. This is applied to obtain microlocal resolvent estimates with no loss compared to the nontrapping setting.
Propriété de symétrie des matrices localisées d'une matrice fortement hyperbolique en un point multiple
Propriétés asymptotiques des vibrations des tores
Propriétés d'oscillation des solutions de l'équation des ondes avec conditions de Dirichlet au bord
Pseudodifferential parametrices of infinite order for SG-hyperbolic problems.
Pseudomonotonicity and nonlinear hyperbolic equations
In this paper we consider a nonlinear hyperbolic boundary value problem. We show that this problem admits weak solutions by using a lifting result for pseudomonotone operators and a surjectivity result concerning coercive and monotone operators.
Qualitative properties of a certain kinetic model of a binary gas.
Quantification asymptotique et microlocalisations d'ordre supérieur. I
Quasilinear hyperbolic 2 x 2 systems with a free, damping boundary condition.
Quasilinear hyperbolic equations with hysteresis
Quasilinear hyperbolic equations with hysteresis
Hysteresis operators are illustrated, and a weak formulation is studied for an initial- and boundary-value problem associated to the equation ; here is a (possibly discontinuous) hysteresis operator, is a second order elliptic operator, is a known function. Problems of this sort arise in plasticity, ferromagnetism, ferroelectricity, and so on. In particular an existence result is outlined.
Quasilinear waves and trapping: Kerr-de Sitter space
In these notes, we will describe recent work on globally solving quasilinear wave equations in the presence of trapped rays, on Kerr-de Sitter space, and obtaining the asymptotic behavior of solutions. For the associated linear problem without trapping, one would consider a global, non-elliptic, Fredholm framework; in the presence of trapping the same framework is available for spaces of growing functions only. In order to solve the quasilinear problem we thus combine these frameworks with the normally...
Quasilineare Differentialgleichungen zweiter Ordnung vom hyperbolischen Typus. Gemischte Randwertaufgaben