Remarques sur l'homogénéisation de certains problèmes quasi-linéaires
Remarques sur l'optique géométrique non linéaire multidimensionnelle
Rigorous derivation of Korteweg-de Vries-type systems from a general class of nonlinear hyperbolic systems
Rigorous derivation of Korteweg-de Vries-type systems from a general class of nonlinear hyperbolic systems
In this paper, we study the long wave approximation for quasilinear symmetric hyperbolic systems. Using the technics developed by Joly-Métivier-Rauch for nonlinear geometrical optics, we prove that under suitable assumptions the long wave limit is described by KdV-type systems. The error estimate if the system is coupled appears to be better. We apply formally our technics to Euler equations with free surface and Euler-Poisson systems. This leads to new systems of KdV-type.
Scalar boundary value problems on junctions of thin rods and plates
We derive asymptotic formulas for the solutions of the mixed boundary value problem for the Poisson equation on the union of a thin cylindrical plate and several thin cylindrical rods. One of the ends of each rod is set into a hole in the plate and the other one is supplied with the Dirichlet condition. The Neumann conditions are imposed on the whole remaining part of the boundary. Elements of the junction are assumed to have contrasting properties so that the small parameter, i.e. the relative...
s∗-compressibility of the discrete Hartree-Fock equation
The Hartree-Fock equation is widely accepted as the basic model of electronic structure calculation which serves as a canonical starting point for more sophisticated many-particle models. We have studied the s∗-compressibility for Galerkin discretizations of the Hartree-Fock equation in wavelet bases. Our focus is on the compression of Galerkin matrices from nuclear Coulomb potentials and nonlinear terms in the Fock operator which hitherto has not been discussed in the literature. It can be shown...
s∗-compressibility of the discrete Hartree-Fock equation
The Hartree-Fock equation is widely accepted as the basic model of electronic structure calculation which serves as a canonical starting point for more sophisticated many-particle models. We have studied the s∗-compressibility for Galerkin discretizations of the Hartree-Fock equation in wavelet bases. Our focus is on the compression of Galerkin matrices from nuclear Coulomb potentials and nonlinear terms in the Fock operator which hitherto has not been discussed in the literature. It can be shown...
Second-order boundary estimates for solutions to singular elliptic equations in borderline cases.
Second-order boundary estimates for solutions to singular elliptic equations.
Second-order estimates for boundary blowup solutions of special elliptic equations.
Selfadjoint Extensions for the Elasticity System in Shape Optimization
Two approaches are proposed to modelling of topological variations in elastic solids. The first approach is based on the theory of selfadjoint extensions of differential operators. In the second approach function spaces with separated asymptotics and point asymptotic conditions are introduced, and a variational formulation is established. For both approaches, accuracy estimates are derived.
Short-time Asymptotics of the two-Dimensional wave Equation for an Annular Vibrating Membrane with Piecewise smooth Boundary Conditions
Singularités d'arêtes pour les problèmes aux limites elliptiques
Some remarks on two-scale convergence and periodic unfolding
The paper discusses some aspects of the adjoint definition of two-scale convergence based on periodic unfolding. As is known this approach removes problems concerning choice of the appropriate space for admissible test functions. The paper proposes a modified unfolding which conserves integral of the unfolded function and hence simplifies the proofs and its application in homogenization theory. The article provides also a self-contained introduction to two-scale convergence and gives ideas for generalization...
Spectral projection, residue of the scattering amplitude and Schrödinger group expansion for barrier-top resonances
We study the spectral projection associated to a barrier-top resonance for the semiclassical Schrödinger operator. First, we prove a resolvent estimate for complex energies close to such a resonance. Using that estimate and an explicit representation of the resonant states, we show that the spectral projection has a semiclassical expansion in integer powers of , and compute its leading term. We use this result to compute the residue of the scattering amplitude at such a resonance. Eventually, we...
Structure of distribution null-solutions to Fuchsian partial differential equations
Sur la propagation de quasi-singularités
Sur l’équation de Prandtl
L’objet de cette note est le problème de Cauchy pour l’équation de Prandtl, dans des espaces de régularité Sobolev. Nous discutons de façon synthétique des résultats récents [4], établissant le caractère fortement linéairement mal posé de ce problème.
Sur l'hamiltonien effectif associé à l'opérateur de Schrödinger magnétique avec potentiel périodique
The asymptotic behaviour of surfaces with prescribed mean curvature near meeting points of fixed and free boundaries
We study the shape of stationary surfaces with prescribed mean curvature in the Euclidean 3-space near boundary points where Plateau boundaries meet free boundaries. In deriving asymptotic expansions at such points, we generalize known results about minimal surfaces due to G. Dziuk. The main difficulties arise from the fact that, contrary to minimal surfaces, surfaces with prescribed mean curvature do not meet the support manifold perpendicularly along their free boundary, in general.