Displaying similar documents to “Hyperbolic equations with non-Lipschitz coefficients.”

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).

Non-Lipschitz coefficients for strictly hyperbolic equations

Fumihiko Hirosawa, Michael Reissig (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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In the present paper we explain the classification of oscillations and its relation to the loss of derivatives for a homogeneous hyperbolic operator of second order. In this way we answer the open question if the assumptions to get C ∞ well posedness for weakly hyperbolic Cauchy problems or for strictly hyperbolic Cauchy problems with non-Lipschitz coefficients are optimal.