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
Stability of discrete shocks for difference approximations to systems of conservation laws.
Stability of hydrodynamic model for semiconductor
In this paper we study the stability of transonic strong shock solutions of the steady state one-dimensional unipolar hydrodynamic model for semiconductors in the isentropic case. The approach is based on the construction of a pseudo-local symmetrizer and on the paradifferential calculus with parameters, which combines the work of Bony-Meyer and the introduction of a large parameter.
Structure of entropy solutions to the eikonal equation