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Large time behaviour of solutions to a class of non-autonomous, degenerate parabolic equations

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Abstract

We consider a class of non-autonomous, degenerate parabolic equations and we study the asymptotic behaviour of the solutions. Even if the equation depends explicitly upon the time, we prove that several asymptotic properties, valid for the autonomous case, are preserved in this more general situation. To our knowledge, it is the first time that the asymptotic behaviour of solutions to non-autonomous equations is studied.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università di Cagliari, Viale Merello 92, 09123, Cagliari, Italy

    F. Ragnedda & S. Vernier Piro

  2. Dipartimento di Matematica “U. Dini”, Università di Firenze, viale Morgagni 67/a, 50134, Florence, Italy

    V. Vespri

Authors
  1. F. Ragnedda
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  2. S. Vernier Piro
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  3. V. Vespri
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Correspondence to F. Ragnedda.

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Ragnedda, F., Vernier Piro, S. & Vespri, V. Large time behaviour of solutions to a class of non-autonomous, degenerate parabolic equations. Math. Ann. 348, 779–795 (2010). https://doi.org/10.1007/s00208-010-0496-4

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  • DOI: https://doi.org/10.1007/s00208-010-0496-4

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