Classes d'opérateurs faiblement hyperboliques non linéaires
Classical conormal, semilinear waves
Classical solutions of hyperbolic partial differential equations with implicit mixed derivative
Classical solutions of the perturbed wave equation with singular potential.
Classical solutions to the scalar conservation law with discontinuous initial data
Sufficient and necessary conditions for the existence and uniqueness of classical solutions to the Cauchy problem for the scalar conservation law are found in the class of discontinuous initial data and non-convex flux function. Regularity of rarefaction waves starting from discontinuous initial data and their dependence on the flux function are investigated and illustrated in a few examples.
Coherent and focusing multidimensional nonlinear geometric optics
Coherent nonlinear waves and the Wiener algebra
We study oscillatory solutions of semilinear first order symmetric hyperbolic system , with real analytic .The main advance in this paper is that it treats multidimensional problems with profiles that are almost periodic in with only the natural hypothesis of coherence.In the special case where has constant coefficients and the phases are linear, the solutions have asymptotic descriptionwhere the profile is almost periodic in .The main novelty in the analysis is the space of profiles which...
Colombeau's theory and shock wave solutions for systems of PDEs.
Compacité par compensation pour une classe de systèmes hyperboliques de p ≥ 3 lois de conservation.
We are concerned with a strictly hyperbolic system of conservation laws ut + f(u)x = 0, where u runs in a region Ω of Rp, such that two of the characteristic fields are genuinely non-linear whereas the other ones are of Blake Temple's type. We begin with the case p = 3 and show, under more or less technical assumptions, that the approximate solutions (uε)ε>0 given either by the vanishing viscosity method or by the Godunov scheme converge to weak entropy solutions as ε goes to 0. The first...
Compacité par compensation trilinéaire et optique géométrique non linéaire
Compact attractors for time-periodic age-structured population models.
Compactness of bounded quasientropy solutions to the system of equations of an isothermal gas.
Comparison of exact and approximate causal solutions of a model curved-space wave equation
Comparison of solutions and successive approximations in the theory of the equation [Book]
Comparison of Some Solution Concepts for Linear First-order Hyperbolic Differential Equations With Non-smooth Coefficients
Comparison theorems for ultrahyperbolic equations.
Compensated compactness and one-dimensional elastodynamics
Compensated compactness and time-periodic solutions to non-autonomous quasilinear telegraph equations
In the present paper, the existence of a weak time-periodic solution to the nonlinear telegraph equation with the Dirichlet boundary conditions is proved. No “smallness” assumptions are made concerning the function . The main idea of the proof relies on the compensated compactness theory.
Complétude asymptotique pour l'équation des ondes dans une classe d'espaces-temps stationnaires et asymptotiquement plats
En utilisant une méthode dépendante du temps, nous démontrons la complétude asymptotique pour l'équation des ondes dans une classe d'espaces-temps stationnaires et asymptotiquement plats. On introduit l'observable de vitesse asymptotique et on décrit son spectre (sous des hypothèses plus faibles que pour la complétude asymptotique). Les méthodes utilisées sont inspirées par celles de l'analyse du problème à deux corps en mécanique quantique.
Comportement asymptotique de la phase de diffusion pour des obstacles non-convexes