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

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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.

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Authors and Affiliations

  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.be, , , , , , BE

    Günter Lumer

  2. FB Mathematik und Informatik, Martin-Luther-Universität, Theodor-Lieser-Str. 5, 06120 Halle, Germany, e-mail: roland@euler.mathematik.uni-halle.de, , , , , , DE

    Roland Schnaubelt

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  1. Günter Lumer
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  2. Roland Schnaubelt
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Received January 10, 2001; accepted April 5, 2001.

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Lumer, G., Schnaubelt, R. Time-dependent parabolic problems on non-cylindrical domains with inhomogeneous boundary conditions. J.evol.equ. 1, 291–309 (2001). https://doi.org/10.1007/PL00001372

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  • DOI: https://doi.org/10.1007/PL00001372

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