Interior estimates in the theory of partial differential equations and their application to initial value problems.
Le théorème de Nishida pour le problème de Cauchy abstrait par une méthode de point fixe
Microlocal tempered inverse image and Cauchy problem.
Microlocalisation simultanée et problème de Cauchy ramifié
Monogenic functions on surfaces.
Necessary and sufficient condition for existence and uniqueness of the solution of Cauchy problem for holomorphic Fuchsian operators.
Nonanalyticity of solutions to
It is proved that the solution to the initial value problem , u(0,x) = 1/(1+x²), does not belong to the Gevrey class in time for 0 ≤ s < 1. The proof is based on an estimation of a double sum of products of binomial coefficients.
On a theorem of Cauchy-Kovalevskaya type for a class of nonlinear PDE's of higher order with deviating arguments
We prove an existence theorem of Cauchy-Kovalevskaya type for the equation where f is a polynomial with respect to the last k variables.
On analytic solutions to the generalized Cauchy problem with data on three surfaces for a quasilinear system.
On functional linear partial differential equations in Gevrey spaces of holomorphic functions.
We investigate existence and unicity of global sectorial holomorphic solutions of functional linear partial differential equations in some Gevrey spaces. A version of the Cauchy-Kowalevskaya theorem for some linear partial -difference-differential equations is also presented.
Plane wave decompositions of monogenic functions
Problème de Cauchy microdifférentiel
Problème de Cauchy pour les hyperfonctions à croissance
Problème de Cauchy pour les systèmes d'équations différentielles et microdifférentielles dans le domaine complexe
Problème de Cauchy pour les systèmes d'équations différentielles et microdifférentielles dans le domaine complexe
Problème de Cauchy ramifié: racine caractéristique triple en involution
Problèmes de Cauchy pseudo-différentiels analytiques non linéaires
Sur le théorème de Cauchy-Kowalewski
Sur quelques équations du type Schrödinger
The Cauchy problem for systems through the normal form of systems and theory of weighted determinant
The author propose what is the principal part of linear systems of partial differential equations in the Cauchy problem through the normal form of systems in the meromorphic formal symbol class and the theory of weighted determinant. As applications, he choose the necessary and sufficient conditions for the analytic well-posedness ( Cauchy-Kowalevskaya theorem ) and well-posedness (Levi condition).