Abstract
AbstractWe consider the problem of maximal regularity for the semilinear non-autonomous evolution equations $$\begin{aligned} u'(t)+A(t)u(t)=F(t,u),\, t \text {-a.e.}, \, u(0)=u_0. \end{aligned}$$
u
′
(
t
)
+
A
(
t
)
u
(
t
)
=
F
(
t
,
u
)
,
t
-a.e.
,
u
(
0
)
=
u
0
.
Here, the time-dependent operators A(t) are associated with (time dependent) sesquilinear forms on a Hilbert space $$\mathcal {H}.$$
H
.
We prove the maximal regularity result in temporally weighted $$L^2$$
L
2
-spaces and other regularity properties for the solution of the previous problem under minimal regularity assumptions on the forms, the initial value $$u_0$$
u
0
and the inhomogeneous term F. Our results are motivated by boundary value problems.
Publisher
Springer Science and Business Media LLC
Reference16 articles.
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2. Achache, M.; Ouhabaz, E.M.: Non-autonomous right and left multiplicative perturbations and maximal regularity. Stud. Math. 242(1), 1–30 (2018)
3. Achache, M.; Ouhabaz, E.M.: Lions’ maximal regularity problem with $$H^{1/2}$$-regularity in time. J. Differ. Equ. 266, 3654–3678 (2019)
4. Achache, M.; Tebbani, H.: Non-autonomous maximal regularity in weighted space. Electron. J. Differ. Equ. 124, 1–24 (2020)
5. Achache, M.: Non autonomous maximal regularity for the fractional evolution equations, 2020. To appear in journal of evolution equations. hal-0-2927759 (2020)