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Article Dans Une Revue Studia Mathematica Année : 2017

Non-autonomous right and left multiplicative perturbations and maximal regularity

Résumé

We consider the problem of maximal regularity for non-autonomous Cauchy problems u ′ (t) + B(t)A(t)u(t) + P (t)u(t) = f (t), u(0) = u 0 and u ′ (t) + A(t)B(t)u(t) + P (t)u(t) = f (t), u(0) = u 0. In both cases, the time dependent operators A(t) are associated with a family of sesquilinear forms and the multiplicative left or right perturbations B(t) as well as the additive perturbation P (t) are families of bounded operators on the considered Hilbert space. We prove maximal L p-regularity results and other regularity properties for the solutions of the previous problems under minimal regularity assumptions on the forms and perturbations.
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hal-01340534 , version 1 (01-07-2016)

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Mahdi Achache, El Maati Ouhabaz. Non-autonomous right and left multiplicative perturbations and maximal regularity. Studia Mathematica, 2017. ⟨hal-01340534⟩
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