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Journal of Evolution Equations

, Volume 1, Issue 3, pp 291–309 | Cite as

Time-dependent parabolic problems on non-cylindrical domains with inhomogeneous boundary conditions

  • Günter Lumer
  • Roland Schnaubelt

Abstract.

We study the relationship between the Dirichlet problem and the Cauchy problem with inhomogeneous boundary conditions for local operators. Our results are applied to non-autonomous parabolic problems on non-cylindrical domains.

Key words: Dirichlet problem, parabolic inhomogeneous initial boundary value problem, semigroup, local operator, Cauchy barrier, variable space propagator, non-cylindrical domain. 

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Copyright information

© Birkhäuser Verlag Basel, 2001

Authors and Affiliations

  • Günter Lumer
    • 1
  • Roland Schnaubelt
    • 2
  1. 1.Institut de Mathématique, Université de Mons-Hainaut, Place du Parc 20, 7000 Mons, Belgium¶and¶Solvay Institutes for Physics and Chemistry, Brussels, Belgium, e-mail: dufour@umh.ac.beBE
  2. 2.FB Mathematik und Informatik, Martin-Luther-Universität, Theodor-Lieser-Str. 5, 06120 Halle, Germany, e-mail: roland@euler.mathematik.uni-halle.deDE

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