Periodic solutions to Maxwell equations in nonlinear media
Periodic solutions to the inhomogeneous sine-Gordon equation
Periodic solutions to weakly nonlinear autonomous wave equations
Perron-Frobenius operators and the Klein-Gordon equation
For a smooth curve and a set in the plane , let be the space of finite Borel measures in the plane supported on , absolutely continuous with respect to the arc length and whose Fourier transform vanishes on . Following [12], we say that is a Heisenberg uniqueness pair if . In the context of a hyperbola , the study of Heisenberg uniqueness pairs is the same as looking for uniqueness sets of a collection of solutions to the Klein-Gordon equation. In this work, we mainly address the...
Perte de régularité pour les équations d’ondes sur-critiques
On prouve que le problème de Cauchy local pour l’équation d’onde sur-critique dans , , impair, avec et , est mal posé dans pour tout , où est l’exposant critique.
Perturbation of a solitary wave of the nonlinear Klein-Gordon equation.
Perturbations singulières coercives : réduction à des perturbations régulières et applications
Perturbations singulières d'équations hyperboliques du second ordre non linéaires
Perturbations singulières pour une équation hyperbolique dégénérée
Perturbations visqueuses de problèmes mixtes hyperboliques et couches limites
Ce travail concerne le problème de Cauchy-Dirichlet pour des systèmes hyperboliques semilinéaires multidimensionnels perturbés par une “petite viscosité". Les solutions considérées sont et locales en temps, le but étant de décrire le comportement de la solution lorsque le paramètre de viscosité () tend vers zéro. Il s’agit d’un problème de perturbation singulière pour lequel une “couche limite" se forme au voisinage du bord. Par des méthodes inspirées de l’optique géométrique non linéaire, nous...
Planar binary trees and perturbative calculus of observables in classical field theory
Plane waves in thermoelasticity with one relaxation time.
Poches de tourbillon et structure géométrique dans les fluides incompressibles bidimensionnels
Poincaré-invariant structures in the solution manifold of a nonlinear wave equation.
The solution manifold M of the equation ⎯φ + gφ3 = 0 in Minkowski space is studied from the standpoint of the establishment of differential-geometric structures therein. It is shown that there is an almost Kähler structure globally defined on M that is Poincaré invariant. In the vanishing curvature case g = 0 the structure obtained coincides with the complex Hilbert structure in the solution manifold of the real wave equation. The proofs are based on the transfer of the equation to an ambient universal...
Pointwise controllability as limit of internal controllability for the wave equation in one space dimension.
Pointwise decay for solutions of the 2D Neumann exterior problem for the wave equation. II
Pointwise decay for solutions of the 2D Neumann exterior problem for the wave equation
We consider the exterior problem in the plane for the wave equation with a Neumann boundary condition. We are interested to the asymptotic behavior for large times for the solution, and in particular to the dependence on the norms of the initial data in the estimate for the pointwise decay rate. In the paper we prove such an estimate, by a combination of the estimate of the local energy decay and decay estimates for the free space solution.
Pointwise Fourier Inversion: a Wave Equation Approach.
Pointwise Fourier Inversion on Tori and Other Compact Manifolds.
Polyhomogeneous solutions of wave equations in the radiation regime
While the physical properties of the gravitational field in the radiation regime are reasonably well understood, several mathematical questions remain unanswered. The question here is that of existence and properties of gravitational fields with asymptotic behavior compatible with existence of gravitational radiation. A framework to study those questions has been proposed by R. Penrose (R. Penrose, “Zero rest-mass fields including gravitation”, Proc. Roy. Soc. London A284 (1965), 159-203), and developed...