Energy estimates for weakly hyperbolic systems of the first order
M. Dreher and I. Witt
Abstract.
For a class of first-order weakly hyperbolic pseudodifferential systems with
finite time degeneracy, well-posedness of the Cauchy problem is proved in an
adapted scale of Sobolev spaces. These Sobolev spaces are constructed in
correspondence to the hyperbolic operator under consideration, making use of
ideas from the theory of elliptic boundary value problems on manifolds with
singularities. In addition, an upper bound for the loss of regularity that
occurs when passing from the Cauchy data to the solutions is established. In
many examples, this upper bound turns out to be sharp.
Communications in Contemporary Mathematics
Vol. 7, No. 6
(2005),
809-837.
The paper is available here:
pdf.
