Maximal regularity for non-autonomous Cauchy problems in weighted spaces
Date
2020-12-20
Authors
Mahdi, Achache
Hossni, Tebbani
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We consider the regularity for the non-autonomous Cauchy problem
u′(t) + A(t)u(t) = ƒ(t) (t ∈ [0, τ]), u(0) = u0.
The time dependent operator A(t) is associated with (time dependent) sesquilinear forms on a Hilbert space H. We prove the maximal regularity result in temporally weighted L2-spaces and other regularity properties for the solution of the problem under minimal regularity assumptions on the forms and the initial value u0. Our results are motivated by boundary value problems.
Description
Keywords
Maximal regularity, Non-autonomous evolution equation, Weighted space
Citation
Mahdi, A., & Hossni, T. (2020). Maximal regularity for non-autonomous Cauchy problems in weighted spaces. <i>Electronic Journal of Differential Equations, 2020</i>(124), pp. 1-24.
Rights
Attribution 4.0 International