Maximal regularity for non-autonomous Cauchy problems in weighted spaces
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 regular...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2020-12-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2020/124/abstr.html |
| Summary: | 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. |
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| ISSN: | 1072-6691 |