Semilinear Hyperbolic Systems and Equations with Singular Initial Data.
Semilinear hyperbolic systems in one space dimension with strongly singular initial data.
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.
Smooth approximations of global in time solutions to scalar conservation laws.
Smoothly symmetrizable hyperbolic systems of partial differential equations.
Solution of a mathematical model of a single piston pump with a more detailed description of the valve function
In this paper a mathematical model of a fluid flow in a tube with a valve and a pump is solved. The function of the valve is described in more detail than in [3], thus making the model more complete.
Solutions classiques globales des équations d'Euler pour un fluide parfait compressible
Soit , , , et les variables usuelles qui décrivent l’état d’un fluide en coordonnées eulériennes. Le domaine physique occupé par le fluide est a priori tout entier, mais peut être nul en dehors d’un compact . On choisit l’équation d’état d’un gaz parfait, , où est une constante. Le cas est celui du gaz mono-atomique.Dans la limite , les collisions sont rares et on est tenté d’approcher le mouvement des particules par un mouvement rectiligne uniforme : le champ de vitesse obéit alors...
Solutions faibles globales pour un modèle d'écoulements diphasiques
Solutions oscillantes des équations de Carleman
Some remarks on time-dependent evolution systems in the hyperbolic case
Some results on the well-posedness for systems with time dependent coefficients
We consider hyperbolic systems with time dependent coefficients and size or . We give some sufficient conditions in order the Cauchy Problem to be well-posed in and in Gevrey spaces.
Stability and Accuracy for Implicit Semidiscretizations of Hyperbolic Problems.
Stability of contact discontinuities under perturbations of bounded variation
Symmetrization of the nonlinear system of gas dynamics equations.
Systèmes de lois de conservation et stabilité BV
Systèmes hyperboliques à multiplicité constante
Systèmes hyperboliques non linéaires
The Cauchy problem for coupled Yang-Mills and scalar fields in the Lorentz gauge
The Cauchy problem for hyperbolic systems with Hölder continuous coefficients with respect to the time variable
We discuss the local existence and uniqueness of solutions of certain nonstrictly hyperbolic systems, with Hölder continuous coefficients with respect to time variable. We reduce the nonstrictly hyperbolic systems to the parabolic ones and by use of the Tanabe-Sobolevski’s method and the Banach scale method we construct a semi-group which gives a representation of the solution to the Cauchy problem.