Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9501634 | Journal of Differential Equations | 2005 | 36 Pages |
Abstract
The aim of this paper is to give an uniform approach to different kinds of degenerate hyperbolic Cauchy problems. We prove that a weakly hyperbolic equation, satisfying an intermediate condition between effective hyperbolicity and the Câ Levi condition, and a strictly hyperbolic equation with non-regular coefficients with respect to the time variable can be reduced to first-order systems of the same type. For such a kind of systems, we prove an energy estimate in Sobolev spaces (with a loss of derivatives) which gives the well-posedness of the Cauchy problem in Câ. In the strictly hyperbolic case, we also construct the fundamental solution and we describe the propagation of the space singularities of the solution which is influenced by the non-regularity of the coefficients with respect to the time variable.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Alessia Ascanelli, Massimo Cicognani,