ACHACHE, Mahdi

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ACHACHE, Mahdi
Institut de Mathématiques de Bordeaux [IMB]

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We consider the problem of maximal regularity for the semilinear non-autonomous fractional equations n i=1 λ i ∂ α i (u − u 0)(t) + A(t)u(t) = F (t, u(t)), t-a.e. Here, ∂ α i denotes the Riemann-Liouville fractional derivative of order α i ∈ (0, 1) w.r.t. time and the time dependent operators A(t) : V → V ′ are associated with (time dependent) sesquilinear forms on a Hilbert space H such that V is continuously and densely embedded into 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, the initial data u 0 and the inhomogeneous term F.< Réduire

Mots clés en anglais

Fractional equations

maximal regularity

non-autonomous evolution equations

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On non-autonomous fractional evolution equations and applications

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Résumé en anglais

Mots clés en anglais

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