Temps d’existence pour l’équation de Klein-Gordon semi-linéaire à données petites faiblement décroissantes
The Cauchy problem for nonlinear wave equations in the homogeneous Sobolev space
The Cauchy problem for the coupled Klein-Gordon-Schrödinger system
We consider the Cauchy problem for a generalized Klein-Gordon-Schrödinger system with Yukawa coupling. We prove the existence of global weak solutions by the compactness method and, through a special choice of the admissible pairs to match two types of equations, we prove the uniqueness of those solutions by an approach similar to the method presented by J. Ginibre and G. Velo for the pure Klein-Gordon equation or pure Schrödinger equation. Though it is very simple in form, the method has an unnatural...
The Cauchy problem for wave equations with non Lipschitz coefficients; Application to continuation of solutions of some nonlinear wave equations
In this paper we study the Cauchy problem for second order strictly hyperbolic operators of the form when the coefficients of the principal part are not Lipschitz continuous, but only “Log-Lipschitz” with respect to all the variables. This class of equation is invariant under changes of variables and therefore suitable for a local analysis. In particular, we show local existence, local uniqueness and finite speed of propagation for the noncharacteristic Cauchy problem. This provides an invariant...
The critical case for a semilinear weakly hyperbolic equation.
The critical nonlinear wave equation in two space dimensions
Extending our previous work, we show that the Cauchy problem for wave equations with critical exponential nonlinearities in 2 space dimensions is globally well-posed for arbitrary smooth initial data.
The geometric optics for a class of hyperbolic second order operators with Hölder continuous coefficients with respect to time
The global Cauchy problem for the non linear Klein-Gordon equation-II
The Picard-Ionescu problem for hyperbolic inclusions with modified argument
We consider the Picard-Ionescu problem for hyperbolic inclusions with modified argument. Existence of a local solution is proved and some properties of the set of solutions are established.
The problem of regular isometric embeddings and the Monge-Ampère equation of hyperbolic type
The Semilinear Second-Order Hyperbolic Equation with Data Strongly Singular at One Point.
The simplified Wheeler-Dewitt equation : the Cauchy problem and some spectral properties
Time Decay for Nonlinear Wave Equations in Two Space Dimensions.
Two new approaches for construction of the high order of accuracy difference schemes for hyperbolic differential equations.