Hyperbolic Cauchy problem and Leray's residue formula

On the Cauchy Problem for Nonlinear Hyperbolic Systems

This paper consider various examples of metrics which are contractive w.r.t. an evolution semigroup, and discusses the possibility of an abstract O.D.E. theory on metric spaces, with applications to hyperbolic systems. In particular, using a recently introduced deenition of Viscosity Solutions, it is shown how a strictly hyperbolic system of conservation laws can be reformulated as an abstract ...

A timelike Cauchy problem and an inverse problem for general hyperbolic equations

Cauchy ’ s theorem , Cauchy ’ s formula , corollaries Paul

Precise Finite Speed and Uniqueness in the Cauchy Problem for Symmetrizable Hyperbolic Systems

Precise finite speed, in the sense of that the domain of influence is a subset of the union of influence curves through the support of the initial data is proved for hyperbolic systems symmetrized by pseudodifferential operators in the spatial variables. From this, uniqueness in the Cauchy problem at spacelike hypersurfaces is derived by a Hölmgren style duality argument. Sharp finite speed is ...

Flat Spacetimes with Compact Hyperbolic Cauchy Surfaces

We study the flat (n+1)-spacetimes Y admitting a Cauchy surface diffeomorphic to a compact hyperbolic n-manifold M . Roughly speaking, we show how to construct a canonical future complete one, Yρ, among all such spacetimes sharing a same holonomy ρ. We study the geometry of Yρ in terms of its canonical cosmological time (CT). In particular we study the asymptotic behaviour of the level surfaces...