The so-called" Cauchy Problem" has a very long and classical story, from J. Hadamard [7],
IG Petrovski [22], J. Leray [20], L. G~ rding [6].... to, for example, the last results of Ivrii and …

Cet article (1) est consacré à l'étude des opérateurs (pseudo)-différentiels analytiques P
dont la variété caractéristique est régulière, involutive, de codimension M> L Nous …

§ 0. Introduction. Bony and Schapira [1] has proved that the Cauchy problem is well-posed
for hyperbolic operators with variable coefficients in the framework of hyperfunctions. In their …

On considère un opérateur différentiel P (x, D) à partie principale hyperbolique et à
caractéristiques de multiplicité constante. Il est connu que, pour de tels opérateurs, le …

where {t3juj(t)} is a fundamental system of solutions and cj are arbitrary constants. (1-2) Any
hyperfunction solution of the eq Page 1 Japan. J. Math. Vol. 5, No. 2, 1979 Fuchsian type …

Kashiwara and Kawai [16] defined microhyperbolicity and proved that the microlocal Cauchy
problem for microhyperbolic pseudodifferential operators is well-posed in the framework of …

§ 1. Introduction Singularities of solutions of the hyperbolic Cauchy problem have been
investigated by many authors. In these works, Hamilton flows (null bicharacteristic flows) …

The Cauchy-Kowalevski theorem assures that the noncharacteristic Cauchy problem for
partial differential equations with analytic coefficients has a unique local solution (cf Nagumo …

In this paper, which is essentially a survey, we solve the global Cauchy problem on causal
manifolds for hyperbolic systems of linear partial differential equations in the framework of …

The steady-state equation, the parabolic Cauchy problem,, and the hyperbolic problem,,, are
considered, where is a matrix-valued positive selfadjoint second-order partial differential …