Propagation des ondes dans les dièdres
Propagation des singularités pour des opérateurs fuchsiens
Propagation of singularities for a first order semi-linear system in
Quantification asymptotique et microlocalisations d'ordre supérieur. I
Radiation fields
We study the “hyperboloidal Cauchy problem” for linear and semi-linear wave equations on Minkowski space-time, with initial data in weighted Sobolev spaces allowing singular behavior at the boundary, or with polyhomogeneous initial data. Specifically, we consider nonlinear symmetric hyperbolic systems of a form which includes scalar fields with a nonlinearity, as well as wave maps, with initial data given on a hyperboloid; several of the results proved apply to general space-times admitting conformal...
Réflexion et diffraction des singularités analytiques
Régularité analytique des chocs uniformément stables à données analytiques
Remarks on vacuum state and uniqueness of concentration process.
Semilinear wave equations with angularly smooth data
Semilinear waves with cusp singularities
Shock fluctuations in a particle system
Shock waves in gas dynamics.
Singular Asymptotic Expansions and Delta Waves for Burger's Equation.
Singular solutions to systems of conservation laws and their algebraic aspects
We discuss the definitions of singular solutions (in the form of integral identities) to systems of conservation laws such as shocks, δ-, δ’-, and -shocks (n = 2,3,...). Using these definitions, the Rankine-Hugoniot conditions for δ- and δ’-shocks are derived. The weak asymptotics method for the solution of the Cauchy problems admitting δ- and δ’-shocks is briefly described. The algebraic aspects of such singular solutions are studied. Namely, explicit formulas for flux-functions of singular solutions...
Singularity formation in systems of non-strictly hyperbolic equations.
Solutions globales des systèmes paraboliques de lois de conservation
Nous considérons ici des solutions particulières des systèmes paraboliques de lois de conservation dans le domaine ou bien pour :Nous faisons l’hypothèse que le système réduit est hyperbolique. Notre but est la description de l’interaction d’ondes simples, mono-dimensionnelles, le plus souvent deux ondes exactement. L’une d’elle, au moins, est une onde de choc (pour le système réduit) visqueuse (pour le système parabolique). Il y a donc a priori un champ caractéristique vraiment non linéaire....
Some remarks on conservative symmetric-hyperbolic systems governing relativistic theories
Stabilité des chocs faibles
Stabilité d’ondes progressives de lois de conservation scalaires
A powerfull method has been developped in [2] for the study of -stability of travelling waves in conservation laws or more generally in equations which display -contractivity, maximum principle and mass conservation. We recall shortly the general procedure. We also show that it partly applies to the waves of a model of radiating gas. These waves have first been studied by Kawashima and Nishibata [5,6] in a different framework. Therefore, shock fronts for this model are stable under mild perturbations....
Stability of contact discontinuities under perturbations of bounded variation