On non-autonomous fractional evolution equations and applications
Language
en
Document de travail - Pré-publication
English Abstract
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 ...Read more >
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.Read less <
English Keywords
Fractional equations
maximal regularity
non-autonomous evolution equations
Origin
Hal imported