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Stability for non-autonomous linear evolution equations with L p-maximal regularity

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Abstract

We study stability and integrability of linear non-autonomous evolutionary Cauchy-problem

$$(P),\left\{ \begin{gathered} \dot u(t) + A(t)u(t) = f(t) t - a.e. on [0,\tau ] \hfill \\ u(0) = 0, \hfill \\ \end{gathered} \right.$$

where A: [0, τ] → L(X,D) is a bounded and strongly measurable function and X, D are Banach spaces such that . Our main concern is to characterize L p-maximal regularity and to give an explicit approximation of the problem (P).

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Authors and Affiliations

  1. Institute of Applied Analysis, Ulm University, 89069, Ulm, Germany

    Hafida Laasri

  2. FB-C Math, Bergische Universität Wuppertal, Gauss Strasse 20, 42097, Wuppertal, Germany

    Hafida Laasri

  3. Department of Mathematics, University Ibn Zohr, Faculty of Sciences, Agadir, Morocco

    Omar El-Mennaoui

Authors
  1. Hafida Laasri
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  2. Omar El-Mennaoui
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Correspondence to Hafida Laasri.

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This work was financially supported by the Deutscher Akademischer Austauschdienst (DAAD).

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Laasri, H., El-Mennaoui, O. Stability for non-autonomous linear evolution equations with L p-maximal regularity. Czech Math J 63, 887–908 (2013). https://doi.org/10.1007/s10587-013-0060-y

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