Équations de champs non linéaires: Des solutions non nécessairement bornées
Équations hyperboliques non linéaires
Etude des Solutions d΄ une Classe d΄ Equatiens Integrodifferentielles Non lineaires aux Operateurs Hyperboliques Ayant Pour Limites des Fonctionnelles Integrales
Étude numérique des oscillations des systèmes semi-linéaires
Exact boundary observability for quasilinear hyperbolic systems
By means of a direct and constructive method based on the theory of semi-global C1 solution, the local exact boundary observability is established for one-dimensional first order quasilinear hyperbolic systems with general nonlinear boundary conditions. An implicit duality between the exact boundary controllability and the exact boundary observability is then shown in the quasilinear case.
Existence and uniqueness of solutions of quasilinear hyperbolic systems of partial differential-functional equations
Existence d'ondes de raréfaction pour des écoulements isentropiques
Existence globale pour un système hyperbolique semi-linéaire de la théorie cinétique des gaz
Existence of global weak solutions to a symmetrically hyperbolic system with a source.
Existence of quasilinear relaxation shock profiles in systems with characteristic velocities
We revisit the existence problem for shock profiles in quasilinear relaxation systems in the case that the velocity is a characteristic mode, implying that the profile ODE is degenerate. Our result states existence, with sharp rates of decay and distance from the Chapman–Enskog approximation, of small-amplitude quasilinear relaxation shocks. Our method of analysis follows the general approach used by Métivier and Zumbrun in the semilinear case, based on Chapman–Enskog expansion and the macro–micro...
Explosion géométrique pour des systèmes quasi-linéaires
Extended thermodynamics---a theory of symmetric hyperbolic field equations
Extended thermodynamics is based on a set of equations of balance which are supplemented by local and instantaneous constitutive equations so that the field equations are quasi-linear differential equations of first order. If the constitutive functions are subject to the requirements of the entropy principle, one may write them in symmetric hyperbolic form by a suitable choice of fields. The kinetic theory of gases, or the moment theories based on the Boltzmann equation, provide an explicit example...