Global Existence for Quasi-Linear Dissipative Wave Equations with Large Data and Small Parameter.
Global existence for the nonlinear equations of crystal optics
Global existence of solutions for the 1-D radiative and reactive viscous gas dynamics
In this paper, we prove the existence of a global solution to an initial-boundary value problem for 1-D flows of the viscous heat-conducting radiative and reactive gases. The key point here is that the growth exponent of heat conductivity is allowed to be any nonnegative constant; in particular, constant heat conductivity is allowed.
Global smooth solutions of some quasi-linear hyperbolic systems with large data
Global solution of mixed problem for a certain system of nonlinear conservation laws
Global solvability of the mixed problem for first order functional partial differential equations
Godunov method for nonconservative hyperbolic systems
This paper is concerned with the numerical approximation of Cauchy problems for one-dimensional nonconservative hyperbolic systems. The theory developed by Dal Maso et al. [J. Math. Pures Appl.74 (1995) 483–548] is used in order to define the weak solutions of the system: an interpretation of the nonconservative products as Borel measures is given, based on the choice of a family of paths drawn in the phase space. Even if the family of paths can be chosen arbitrarily, it is natural to require this...
Group-theoretical solutions to gas dynamic equations generated by three-dimensional Lie subalgebras.
Homogénéisation d'équations hyperboliques du premier ordre et application aux écoulements miscibles en milieu poreux
Identification of nonlinear coefficient in a transport equation.
Implicit difference method for nonlinear first order partial differential equations.
Infinite systems of first order PFDEs with mixed conditions
We consider mixed problems for infinite systems of first order partial functional differential equations. An infinite number of deviating functions is permitted, and the delay of an argument may also depend on the spatial variable. A theorem on the existence of a solution and its continuous dependence upon initial boundary data is proved. The method of successive approximations is used in the existence proof. Infinite differential systems with deviated arguments and differential integral systems...
Intégrabilité d'une classe de systèmes de lois de conservation.
Interactions trilinéaires résonantes
Interface model coupling via prescribed local flux balance
This paper deals with the non-conservative coupling of two one-dimensional barotropic Euler systems at an interface at x = 0. The closure pressure laws differ in the domains x < 0 and x > 0, and a Dirac source term concentrated at x = 0 models singular pressure losses. We propose two numerical methods. The first one relies on ghost state reconstructions at the interface while the second is based on a suitable relaxation framework. Both methods satisfy a well-balanced property for stationary...
Involutivity and Symple Waves in R^2
A strictly hyperbolic quasi-linear 2×2 system in two independent variables with C2 coefficients is considered. The existence of a simple wave solution in the sense that the solution is a 2-dimensional vector-valued function of the so called Riemann invariant is discussed. It is shown, through a purely geometrical approach, that there always exists simple wave solution for the general system when the coefficients are arbitrary C^2 functions depending on both, dependent and independent variables.
Les équations de Kelvin-Helmotz. Un problème bien posé uniquement dans le cadre analytique
L’existence d’une solution classique d’une éqéaire dans (Communication préalable)
Local existence of solutions for an aggregation equation in Besov spaces
We prove the local in time existence of solutions for an aggregation equation in Besov spaces. The Fourier localization technique and Littlewood-Paley theory are the main tools used in the proof.
Local existence of solutions of the mixed problem for the system of equations of ideal relativistic hydrodynamics
Existence and uniqueness of local solutions for the initial-boundary value problem for the equations of an ideal relativistic fluid are proved. Both barotropic and nonbarotropic motions are considered. Existence for the linearized problem is shown by transforming the equations to a symmetric system and showing the existence of weak solutions; next, the appropriate regularity is obtained by applying Friedrich's mollifiers technique. Finally, existence for the nonlinear problem is proved by the method...