Electronic Journal of Differential Equations, 
Vol. 2020 (2020), No. 124, pp. 1-24.

Title: Maximal regularity for non-autonomous Cauchy problems in weighted spaces
       
Authors: Achache Mahdi (Univ. Bordeaux, Talence, France)
         Tebbani Hossni (Univ. Setif -1-, Algeria)

Abstract:
 We consider the  regularity for the non-autonomous Cauchy problem
 $$
 u'(t) + A(t) u(t) = f(t)\quad (t \in [0, \tau]), \quad u(0) = u_0.
 $$
 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.