in this paper, the goursat problem of a third order equation on cases of explicit solvability isinvestigated, with the help of the riemann function. some results and one theorem are given concerning theexistence and uniqueness for the solution of the suggested problem.

In the last decade, discrete and continuous time processes with lumped and distributed parameters found wide application in the field of mathematical economics and in problems of control dynamic system optimization and differential games [1–19]. The present article is devoted to an investigation of problems of this kind with distributed parameters, where the treatment is in finite-dimensional E...

The whole idea of holography as put forward by Gerard ’t Hooft assumes that data on a boundary determine physics in the volume. This corresponds to a Dirichlet problem for euclidean signature, or to a Goursat (characteristic) problem in the lorentzian setting. Is this last aspect of the problem that is explored here for Ricci flat spaces with vanishing cosmological constant.

In the paper, the bang-bang principle for a control system connected with a system of linear nonautonomous partial differential equations of hyperbolic type (the socalled Goursat-Darboux problem or continuous Fornasini-Marchesini problem) is proved. Some density result is also obtained.

Goursat structures are the dual objects of E. Cartan's \special" systems (also called \en drapeau" in 7]). We prove that the growth vector is not a complete local invariant for a Goursat structure on R n , n 9; and that there exist innnitely many locally non-equivalent Goursat structures on R n , n 10. Sur la classiication locale des structures de Goursat Les structures de Goursat sont les obje...