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Czechoslovak Mathematical Journal

, Volume 63, Issue 4, pp 887–908 | Cite as

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

  • Hafida Laasri
  • Omar El-Mennaoui
Article

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 Open image in new window . Our main concern is to characterize L p -maximal regularity and to give an explicit approximation of the problem (P).

Keywords

maximal regularity on-autonomous evolution equation stability for linear evolution equation integrability for linear evolution equation 

MSC 2010

35K90 47D06 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2013

Authors and Affiliations

  1. 1.Institute of Applied AnalysisUlm UniversityUlmGermany
  2. 2.FB-C MathBergische Universität WuppertalWuppertalGermany
  3. 3.Department of MathematicsUniversity Ibn Zohr, Faculty of SciencesAgadirMorocco

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