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 |
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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 |
| _version_ | 1818870479142780928 |
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| author | Achache Mahdi Tebbani Hossni |
| author_facet | Achache Mahdi Tebbani Hossni |
| author_sort | Achache Mahdi |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-19T12:07:40Z |
| format | Article |
| id | doaj.art-8333daf1a55d40e590620443603b675d |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-19T12:07:40Z |
| publishDate | 2020-12-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-8333daf1a55d40e590620443603b675d2022-12-21T20:22:18ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912020-12-012020124,124Maximal regularity for non-autonomous Cauchy problems in weighted spacesAchache Mahdi0Tebbani Hossni1 Univ. Bordeaux, Talence, France Univ. Setif -1-, Algeria 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.http://ejde.math.txstate.edu/Volumes/2020/124/abstr.htmlmaximal regularitynon-autonomous evolution equationweighted space |
| spellingShingle | Achache Mahdi Tebbani Hossni Maximal regularity for non-autonomous Cauchy problems in weighted spaces Electronic Journal of Differential Equations maximal regularity non-autonomous evolution equation weighted space |
| title | Maximal regularity for non-autonomous Cauchy problems in weighted spaces |
| title_full | Maximal regularity for non-autonomous Cauchy problems in weighted spaces |
| title_fullStr | Maximal regularity for non-autonomous Cauchy problems in weighted spaces |
| title_full_unstemmed | Maximal regularity for non-autonomous Cauchy problems in weighted spaces |
| title_short | Maximal regularity for non-autonomous Cauchy problems in weighted spaces |
| title_sort | maximal regularity for non autonomous cauchy problems in weighted spaces |
| topic | maximal regularity non-autonomous evolution equation weighted space |
| url | http://ejde.math.txstate.edu/Volumes/2020/124/abstr.html |
| work_keys_str_mv | AT achachemahdi maximalregularityfornonautonomouscauchyproblemsinweightedspaces AT tebbanihossni maximalregularityfornonautonomouscauchyproblemsinweightedspaces |