| Title:
|
Evolution equations governed by Lipschitz continuous non-autonomous forms (English) |
| Author:
|
Sani, Ahmed |
| Author:
|
Laasri, Hafida |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
65 |
| Issue:
|
2 |
| Year:
|
2015 |
| Pages:
|
475-491 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove $L^2$-maximal regularity of the linear non-autonomous evolutionary Cauchy \rlap {problem} $$ \dot {u} (t)+A(t)u(t)=f(t) \quad \text {for a.e.\ } t\in [0,T],\quad u(0)=u_0, $$ where the operator $A(t)$ arises from a time depending sesquilinear form $\mathfrak {a}(t,\cdot ,\cdot )$ on a Hilbert space $H$ with constant domain $V.$ We prove the maximal regularity in $H$ when these forms are time Lipschitz continuous. We proceed by approximating the problem using the frozen coefficient method developed by El-Mennaoui, Keyantuo, Laasri (2011), El-Mennaoui, Laasri (2013), and Laasri (2012). As a consequence, we obtain an invariance criterion for convex and closed sets of $H.$ (English) |
| Keyword:
|
sesquilinear form |
| Keyword:
|
non-autonomous evolution equation |
| Keyword:
|
maximal regularity |
| Keyword:
|
convex set |
| MSC:
|
35B65 |
| MSC:
|
35K45 |
| MSC:
|
35K90 |
| MSC:
|
47D06 |
| idZBL:
|
Zbl 06486959 |
| idMR:
|
MR3360439 |
| DOI:
|
10.1007/s10587-015-0188-z |
| . |
| Date available:
|
2015-06-16T17:58:36Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144282 |
| . |
| Reference:
|
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