Energy estimates for weakly hyperbolic systems of the first order

Michael Dreher, Ingo Witt

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

For a class of first-order weakly hyperbolic pseudo-differential 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.

Original languageEnglish
Pages (from-to)809-837
Number of pages29
JournalCommunications in Contemporary Mathematics
Volume7
Issue number6
DOIs
Publication statusPublished - Dec 2005

Keywords

  • weakly hyperbolic systems
  • coefficients depending on the spatial variables
  • well-posedness of the Cauchy problem in Sobolev-type spaces
  • loss of regularity
  • SINGULARITIES
  • PROPAGATION
  • OPERATORS
  • EQUATIONS

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