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...
Finite volume schemes for nonlinear parabolic problems: another regularization method
First order partial functional differential equations with unbounded delay.
Formes bilinéaires compatibles avec un système hyperbolique et problème de Cauchy
Fundamental solutions and singular shocks in scalar conservation laws.
We study the existence and non-existence of fundamental solutions for the scalar conservation laws ut + f(u)x = 0, related to convexity assumptions on f. We also study the limits of those solutions as the initial mass goes to infinity. We especially prove the existence of so-called Friendly Giants and Infinite Shock Solutions according to the convexity of f, which generalize the explicit power case f(u) = um. We introduce an extended notion of solution and entropy criterion to allow infinite shocks...
Gasdynamic regularity: some classifying geometrical remarks.
Generalized method of lines for first order partial functional differential equations
Classical solutions of initial boundary value problems are approximated by solutions of associated differential difference problems. A method of lines for an unknown function for the original problem and for its partial derivatives with respect to spatial variables is constructed. A complete convergence analysis for the method is given. A stability result is proved by using differential inequalities with nonlinear estimates of the Perron type for the given operators. A discretization...
Generalized n-dimensional Gronwall's inequality and its applications to non-selfadjoint and non-linear hyperbolic equations
Generalized periodic solutions of nonlinear telegraph equations (Preliminary communication)
Generalized Solution to a Semilinear Hyperbolic System with a Non-Lipshitz Nonlinearity.
Generalized solutions describing singularity interaction.
Generalized solutions of mixed problems for quasilinear hyperbolic systems of functional partial differential equations in the Schauder canonic form
Generalized Solutions to Semilinear Hyperbolic Systems.
Geometric optics with critical vanishing viscosity for one-dimensional semilinear initial value problems.
Global boundary controllability of the de St. Venant equations between steady states
Global classical solutions to a kind of mixed initial-boundary value problem for inhomogeneous quasilinear hyperbolic systems
In this paper, the mixed initial-boundary value problem for inhomogeneous quasilinear strictly hyperbolic systems with nonlinear boundary conditions in the first quadrant is investigated. Under the assumption that the right-hand side satisfies a matching condition and the system is strictly hyperbolic and weakly linearly degenerate, we obtain the global existence and uniqueness of a solution and its stability with certain small initial and boundary data.