Some Necessary Conditions for Hyperbolic Systems
In this article some necessary conditions in order for the Cauchy problem for hyperbolic systems to be well posed will be studied. In the scalar case, from Ivrii-Petkov , for the well-posedness of the Cauchy problem, a set of vanishing conditions on the lower order terms must be verified at a multiple characteristic. Our purpose is to find some necessary conditions which correspond to the Ivrii-Petkov conditions for systems. In , we obtained a necessary condition in this direction. Here we continue this study.
KeywordsCauchy Problem Differential Operator Asymptotic Solution Hyperbolic System Scalar Case
Unable to display preview. Download preview PDF.
- V.Ja. Ivrii and V.M. Petkov, Necessary conditions for the Cauchy problem for nonstrictly hyperbolic equations to be well posed, Uspehi Mat.Nauka, 29 (1974), 3–70.Google Scholar
- A. Bove and T. Nishitani, Necessary conditions for the well posedness of the Cauchy problem for hyperbolic systems, preprint, 1999.Google Scholar