Geodesic
Evolution equations governed by Lipschitz continuous non-autonomous forms
Czechoslovak Mathematical Journal, Tome 65 (2015) no. 2, pp. 475-491.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 $H.$
DOI : 10.1007/s10587-015-0188-z
Classification : 35B65, 35K45, 35K90, 47D06
Keywords: sesquilinear form; non-autonomous evolution equation; maximal regularity; convex set 
@article{10_1007_s10587_015_0188_z,
     author = {Sani, Ahmed and Laasri, Hafida},
     title = {Evolution equations governed by {Lipschitz} continuous non-autonomous forms},
     journal = {Czechoslovak Mathematical Journal},
     pages = {475--491},
     publisher = {mathdoc},
     volume = {65},
     number = {2},
     year = {2015},
     doi = {10.1007/s10587-015-0188-z},
     mrnumber = {3360439},
     zbl = {06486959},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-015-0188-z/}
}
TY  - JOUR
AU  - Sani, Ahmed
AU  - Laasri, Hafida
TI  - Evolution equations governed by Lipschitz continuous non-autonomous forms
JO  - Czechoslovak Mathematical Journal
PY  - 2015
SP  - 475
EP  - 491
VL  - 65
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10587-015-0188-z/
DO  - 10.1007/s10587-015-0188-z
LA  - en
ID  - 10_1007_s10587_015_0188_z
ER  - 
%0 Journal Article
%A Sani, Ahmed
%A Laasri, Hafida
%T Evolution equations governed by Lipschitz continuous non-autonomous forms
%J Czechoslovak Mathematical Journal
%D 2015
%P 475-491
%V 65
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10587-015-0188-z/
%R 10.1007/s10587-015-0188-z
%G en
%F 10_1007_s10587_015_0188_z
Sani, Ahmed; Laasri, Hafida. Evolution equations governed by Lipschitz continuous non-autonomous forms. Czechoslovak Mathematical Journal, Tome 65 (2015) no. 2, pp. 475-491. doi : 10.1007/s10587-015-0188-z. http://geodesic.mathdoc.fr/articles/10.1007/s10587-015-0188-z/

Cité par Sources :