Displaying similar documents to “Hyperbolic Cauchy problem and Leray's residue formula”

On geometry of fronts in wave propagations

Susumu Tanabé (1999)

Banach Center Publications

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We give a geometric descriptions of (wave) fronts in wave propagation processes. Concrete form of defining function of wave front issued from initial algebraic variety is obtained by the aid of Gauss-Manin systems associated with certain complete intersection singularities. In the case of propagations on the plane, we get restrictions on types of possible cusps that can appear on the wave front.

The Cauchy problem for systems through the normal form of systems and theory of weighted determinant

Waichiro Matsumoto (1998-1999)

Séminaire Équations aux dérivées partielles

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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 C ∞ well-posedness (Levi condition).

Asymptotic solutions to Fuchsian equations in several variables

Boris Sternin, Victor Shatalov (1996)

Banach Center Publications

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The aim of this paper is to construct asymptotic solutions to multidimensional Fuchsian equations near points of their degeneracy. Such construction is based on the theory of resurgent functions of several complex variables worked out by the authors in [1]. This theory allows us to construct explicit resurgent solutions to Fuchsian equations and also to investigate evolution equations (Cauchy problems) with operators of Fuchsian type in their right-hand parts.

Hyperbolicity of two by two systems with two independent variables

Tatsuo Nishitani (1998)

Journées équations aux dérivées partielles

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We study the simplest system of partial differential equations: that is, two equations of first order partial differential equation with two independent variables with real analytic coefficients. We describe a necessary and sufficient condition for the Cauchy problem to the system to be C infinity well posed. The condition will be expressed by inclusion relations of the Newton polygons of some scalar functions attached to the system. In particular, we can give a characterization of the...