Electron. J. Differential Equations, Vol. 2020 (2020), No. 124, pp. 1-24.

Maximal regularity for non-autonomous Cauchy problems in weighted spaces

Achache Mahdi, Tebbani Hossni

We consider the regularity for the non-autonomous Cauchy problem

The time dependent operator A(t) is associated with (time dependent) sesquilinear forms on a Hilbert space $\mathcal{H}$. We prove the maximal regularity result in temporally weighted L^2-spaces and other regularity properties for the solution of the problem under minimal regularity assumptions on the forms and the initial value u_0. Our results are motivated by boundary value problems.

Submitted October 9, 2019. Published December 20, 2020.
Math Subject Classifications: 35A23.
Key Words: Maximal regularity; non-autonomous evolution equation; weighted space.

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Achache Mahdi
Department of Mathematics, Univ. Bordeaux
Institut de Mathématiques (IMB). CNRS UMR 5251. 351
Cours de la Libération 33405 Talence, France
email: Mahdi.Achache@math.ubordeaux.fr
Tebbani Hossni
Department of Mathematics
Univ. Séetif -1-, Algeria
email maths47@ymail.com

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