Archiv der Mathematik

, Volume 72, Issue 6, pp 454–460 | Cite as

The non-autonomous Kato class

  • Roland Schnaubelt
  • Jürgen Voigt


We discuss singular time dependent absorption-excitation rates for second order parabolic equations. A suitable class, the non-autonomous Kato class, is defined for the heat equation in connection with the non-autonomous Miyadera perturbation theorem. We give sufficient conditions in terms of integrability for a potential to belong to the non-autonomous Kato class.


Parabolic Equation Kato Heat Equation Suitable Class Perturbation Theorem 


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Copyright information

© Birkhäuser Verlag, Basel 1999

Authors and Affiliations

  • Roland Schnaubelt
    • 1
  • Jürgen Voigt
    • 2
  1. 1.Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, GermanyDeutschland
  2. 2.Technische Universität Dresden, Fachrichtung Mathematik, D-01062 Dresden, GermanyDeutschland

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