Evolution equations governed by Lipschitz continuous non-autonomous forms
Evolution equations governed by Lipschitz continuous non-autonomous forms
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DOI：
10.1007/s10587-015-0188-z
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发表时间：
2014-11
影响因子：
0.5
通讯作者：
A. Sani;H. Laasri
中科院分区：
文献类型：
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作者：
A. Sani;H. Laasri
证明了线性非自治发展柯西问题u（t）+ A（t）u（t）= f（t）{\text{ for a}}{\text{.e}}{\text{. }}t \in \left[ {0，T} \right]，{\text{ }}u（0）= {u_0}$$，其中算子A（t）来自于具有常域V的Hilbert空间H上的依赖于时间的半双线性形式a（t，·，·）。当这些形式是时间Lipschitz连续时，我们证明了H中的极大正则性.我们继续使用El-Mennaoui，Keyantuo，Laasri（2011），El-Mennaoui，Laasri（2013）和Laasri（2012）开发的冻结系数方法来近似问题。作为结果，我们得到了H的凸集和闭集的不变性准则.
We proveL2-maximal regularity of the linear non-autonomous evolutionary Cauchy problem $$\dot u(t) + A(t)u(t) = f(t){\text{ for a}}{\text{.e}}{\text{. }}t \in \left[ {0,T} \right],{\text{ }}u(0) = {u_0}$$, where the operatorA(t)arises from a time depending sesquilinear forma(t, ·, ·) on a Hilbert spaceHwith constant domainV. We prove the maximal regularity inHwhen 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 ofH.