Propriétés asymptotiques des vibrations des tores
Propriétés de certaines solutions d'inégalité aux dérivées partielles de type parabolique
Propriétés de moyenne pour les solutions de systèmes elliptiques
In this article, we consider the set F of functions annihilated by a uniformly elliptic system S in an open set Ω of Rn.We show that, as in the case of harmonic functions, F satisfies a submean-property, first for p=2 by elliptic estimates, then for all p > 0:|∇k u(x)|p ≤ C / (rn+kp) ∫B(x,r) |u(y)|p dyfor each u in F, each k > 0 and every ball B(x,r) included in Ω.As a consequence, we can compare ||u||Lp(Ω) and ||∇ku||Lp(Ω,δkp) where δ is the distance to the boundary of Ω, under the...
Propriétés des courbes intégrales de champs de vecteurs et estimations ponctuelles d'équation elliptiques dégénérés
Propriétés d'oscillation des solutions de l'équation des ondes avec conditions de Dirichlet au bord
Pseudo-differential operators with positive symbols
Pseudo-spectrum for a class of semi-classical operators
We study in this paper a notion of pseudo-spectrum in the semi-classical setting called injectivity pseudo-spectrum. The injectivity pseudo-spectrum is a subset of points in the complex plane where there exist some quasi-modes with a precise rate of decay. For that reason, these values can be considered as some ‘almost eigenvalues’ in the semi-classical limit. We are interested here in studying the absence of injectivity pseudo-spectrum, which is characterized by a global a priori estimate. We prove...
Puits multiples (d'après des travaux avec B. Helffer)
Puits multiples pour l'opérateur de Dirac
Pullback attractors for non-autonomous 2D MHD equations on some unbounded domains
We study the 2D magnetohydrodynamic (MHD) equations for a viscous incompressible resistive fluid, a system with the Navier-Stokes equations for the velocity field coupled with a convection-diffusion equation for the magnetic fields, in an arbitrary (bounded or unbounded) domain satisfying the Poincaré inequality with a large class of non-autonomous external forces. The existence of a weak solution to the problem is proved by using the Galerkin method. We then show the existence of a unique minimal...
Pullback attractors for non-autonomous parabolic equations involving grushin operators.
Pullback attractors for nonautonomous parabolic equations involving weighted p-Laplacian operators
Using the asymptotic a priori estimate method, we prove the existence of pullback attractors for nonautonomous quasilinear degenerate parabolic equations involving weighted p-Laplacian operators in bounded domains, without restriction on the growth order of the polynomial type nonlinearity and on the exponential growth of the external force. The results obtained improve some recent ones for nonautonomous reaction-diffusion equations. Moreover, a relationship between pullback attractors and uniform...
Pullback permanence for non-autonomous partial differential equations.
Pulsating traveling waves in the singular limit of a reaction-diffusion system in solid combustion