SAK principle for a class of Grushin-type operators.
We prove Fefferman's SAK Principle for a class of hypoelliptic operators on R2 whose nonnegative symbol vanishes anisotropically on the characteristic manifold.
Scattering on stratified media: the microlocal properties of the scattering matrix and recovering asymptotics of perturbations
The scattering matrix is defined on a perturbed stratified medium. For a class of perturbations, its main part at fixed energy is a Fourier integral operator on the sphere at infinity. Proving this is facilitated by developing a refined limiting absorption principle. The symbol of the scattering matrix determines the asymptotics of a large class of perturbations.
Schrödinger equation on the Heisenberg group
Selfsimilar profiles in large time asymptotics of solutions to damped wave equations
Large time behavior of solutions to the generalized damped wave equation for is studied. First, we consider the linear nonhomogeneous equation, i.e. with F = F(x,t) independent of u. We impose conditions on the operators A and B, on F, as well as on the initial data which lead to the selfsimilar large time asymptotics of solutions. Next, this abstract result is applied to the equation where , , and the nonlinear term is either or . In this case, the asymptotic profile of solutions is given...
Semiclassical resolvent estimates for two and three-body Schrödinger operators
Series solutions of time-fractional PDEs by homotopy analysis method.
Singular perturbations and parameter-dependent pseudo-differential boundary problems
Singularités des solutions d'équations d'ondes semi-linéaires
Smoothing of dispersive waves
Solution of Cauchy problems modulo flat functions
Solutions analytiques de l'équation d'Euler d'un fluide compressible
Solutions asymptotiques de l'équation de Dirac
Solutions asymptotiques et groupe symplectique
Solutions Globales Régulières pour Quelques Équations Lineaires D'évolution du Type Pseudo-Différentiel Singulier
2000 Mathematics Subject Classification: 35C15, 35D05, 35D10, 35S10, 35S99.We give here examples of equations of type (1) ∂tt2 y -p(t, Dx) y = 0, where p is a singular pseudo-differential operator with regular global solutions when the Cauchy data are regular, t ∈ R, x ∈ R5.
Solutions hyperfonctions du problème de Cauchy
Some decay properties for the damped wave equation on the torus
This article is a proceedings version of the ongoing work [1], and has been the object of a talk of the second author during the Journées “Équations aux Dérivées Partielles” (Biarritz, 2012).We address the decay rates of the energy of the damped wave equation when the damping coefficient does not satisfy the Geometric Control Condition (GCC). First, we give a link with the controllability of the associated Schrödinger equation. We prove that the observability of the Schrödinger group implies that...
Some remarks on almost-positivity of 's
Per una classe di operatori pseudodifferenziali a caratteristiche multiple vengono date condizioni necessarie e sufficienti per la validità di stime dal basso «ottimali»
Some remarks on Weyl pseudodifferential operators
Sous-ellipticité d'opérateurs intégro-différentiels vérifiant le principe du maximum
Sous-ellipticité d'opérateurs intégro-différentiels vérifiant le principe du maximum