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Article Dans Une Revue Journal of Evolution Equations Année : 2022

Non autonomous maximal regularity for the fractional evolution equations

Résumé

We consider the problem of maximal regularity for the semilinear non-autonomous fractional equations B α u(t) + A(t)u(t) = F (t, u), t-a.e. Here, B α denotes the Riemann-Liouville fractional derivative of order α ∈ (0, 1) w.r.t. time and the time dependent operators A(t) are associated with (time dependent) sesquilinear forms on a Hilbert space H. We prove maximal L p-regularity results and other regularity properties for the solutions of the above equation under minimal regularity assumptions on the forms and the inhomogeneous term F.
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Dates et versions

hal-02927759 , version 1 (02-09-2020)

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Achache Mahdi. Non autonomous maximal regularity for the fractional evolution equations. Journal of Evolution Equations, 2022, 22 (2), pp.48. ⟨10.1007/s00028-022-00808-4⟩. ⟨hal-02927759⟩
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