Die Lie'sche Integrationsmethode der partiellen Differentialgleichungen erster Ordnung
Die Lie'sche Integrationsmethode der partiellen Differentialgleichungen erster Ordnung
Difference methods for non-linear partial differential equations of the first order
Differential Games and Nonlinear First Order PDE on Bounded Domains.
Differential operators of the first order with degenerate principal symbols
Let there be given a differential operator on of the form , where is a real matrix and μ is a complex number. We study the following question: To what extent the mapping is surjective? We shall give some conditions on A and μ which assure the surjectivity of D.
Differential procedures for systems of implicit relations and implicitly coupled nonlinear boundary value problems
Diffusion limit of the Lorentz model : asymptotic preserving schemes
This paper deals with the diffusion limit of a kinetic equation where the collisions are modeled by a Lorentz type operator. The main aim is to construct a discrete scheme to approximate this equation which gives for any value of the Knudsen number, and in particular at the diffusive limit, the right discrete diffusion equation with the same value of the diffusion coefficient as in the continuous case. We are also naturally interested with a discretization which can be used with few velocity discretization...
Diffusion Limit of the Lorentz Model: Asymptotic Preserving Schemes
This paper deals with the diffusion limit of a kinetic equation where the collisions are modeled by a Lorentz type operator. The main aim is to construct a discrete scheme to approximate this equation which gives for any value of the Knudsen number, and in particular at the diffusive limit, the right discrete diffusion equation with the same value of the diffusion coefficient as in the continuous case. We are also naturally interested with a discretization which can be used with few velocity discretization...
Discontinuous solutions of deterministic optimal stopping time problems
Domaine d’analycité des solutions de l’équation d’Euler dans un ouvert de
Dunkl hyperbolic equations.
Dynamics of Populations Structured by Internal Variables.
E. E. Levi convexity and the Hans Lewy problem. Part I : reduction to vanishing theorems
Équations de transport à coefficient dont le gradient est donné par une intégrale singulière
Nous rappelons tout d’abord l’approche maintenant classique de renormalisation pour établir l’unicité des solutions faibles des équations de transport linéaires, en mentionnant les résultats récents qui s’y rattachent. Ensuite, nous montrons comment l’approche alternative introduite par Crippa et DeLellis estimant directement le flot lagrangien permet d’obtenir des résultats nouveaux. Nous établissons l’existence et l’unicité du flot associé à une équation de transport dont le coefficient a un gradient...
Équations de transport dont les vitesses sont partiellement
Nous démontrons l’unicité des solutions faibles pour une classe d’équations de transport dont les vitesses sont partiellement à variations bornées. Nous nous intéressons à des champs de vecteurs du typeavec une borne sur la divergence de chacun des champs . Ce modèle a été étudié récemment dans [LL] par C. Le Bris et P.-L. Lions avec une régularité ; nous montrons ici également que, dans le cas , le contrôle de la divergence totale du champ est suffisant. Notre méthode consiste à démontrer...
Estimates of solutions to linear elliptic systems and equations
Whenever nonlinear problems have to be solved through approximation methods by solving related linear problems a priori estimates are very useful. In the following this kind of estimates are presented for a variety of equations related to generalized first order Beltrami systems in the plane and for second order elliptic equations in . Different types of boundary value problems are considered. For Beltrami systems these are the Riemann-Hilbert, the Riemann and the Poincaré problem, while for elliptic...
Estimations hölderiennes pour l'équation d'Euler
Étude d'un problème de transport singulier
Example of solving of the boundary value problems for one partial differential equations with two unknown functions
Existence and Regularity of Solutions for a Semilinear First-Order Equation on the Torus.