Global analytic and Gevrey surjectivity of the Mizohata operator
The surjectivity of the operator from the Gevrey space , , onto itself and its non-surjectivity from to is proved.
Homogenization and localization in locally periodic transport
In this paper, we study the homogenization and localization of a spectral transport equation posed in a locally periodic heterogeneous domain. This equation models the equilibrium of particles interacting with an underlying medium in the presence of a creation mechanism such as, for instance, neutrons in nuclear reactors. The physical coefficients of the domain are -periodic functions modulated by a macroscopic variable, where is a small parameter. The mean free path of the particles is also...
Homogenization and localization in locally periodic transport
In this paper, we study the homogenization and localization of a spectral transport equation posed in a locally periodic heterogeneous domain. This equation models the equilibrium of particles interacting with an underlying medium in the presence of a creation mechanism such as, for instance, neutrons in nuclear reactors. The physical coefficients of the domain are ε-periodic functions modulated by a macroscopic variable, where ε is a small parameter. The mean free path of the particles...
Homogenization of a spectral equation with drift in linear transport
This paper deals with the homogenization of a spectral equation posed in a periodic domain in linear transport theory. The particle density at equilibrium is given by the unique normalized positive eigenvector of this spectral equation. The corresponding eigenvalue indicates the amount of particle creation necessary to reach this equilibrium. When the physical parameters satisfy some symmetry conditions, it is known that the eigenvectors of this equation can be approximated by the product of two...
Homogenization of a spectral equation with drift in linear transport
This paper deals with the homogenization of a spectral equation posed in a periodic domain in linear transport theory. The particle density at equilibrium is given by the unique normalized positive eigenvector of this spectral equation. The corresponding eigenvalue indicates the amount of particle creation necessary to reach this equilibrium. When the physical parameters satisfy some symmetry conditions, it is known that the eigenvectors of this equation can be approximated by the product...
Integral representation of solutions of first-order linear partial differential equations, I
Integral representation of solutions of linear partial differential equations. II
regularity of velocity averages
L'équation Non-homogene de Vécua
Linear Pfaff systems with the lower characteristic vectors' set of positive Lebesgue measure.
Local a priori estimates in Lp for first order linear operators with nonsmooth coefficients.
Lokale Auflösbarkeit von Differentialoperatoren erster Ordnung in einem kritischen Punkt.
Moyennisation des champs de vecteurs et ÉDP
Necessary and sufficient conditions for the local solvability in hyperfunctions of a class of systems of complex vector fields.
Necessary conditions for strong hyperbolicity of first order systems
Neuer und directer Beweis eines Fundamentalsatzes der Invariantentheorie.
Non completely solvable systems of complex first order PDEs
Note on the solution of transport equation by Tau method and Walsh functions.
Noyaux élémentaires d'équations aux dérivées partielles du premier ordre
On analyticity in homogeneous first order partial differential equations