Non-autonomous right and left multiplicative perturbations and maximal regularity
Non-autonomous right and left multiplicative perturbations and maximal regularity
复制标题
非自主右乘和左乘扰动和最大正则性
DOI：
10.4064/sm8721-6-2017
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
E. Ouhabaz
中科院分区：
文献类型：
--
作者：
M. Achache;E. Ouhabaz
我们考虑非自治柯西问题 $u'(t) + B(t)A(t)u(t) + P(t)u(t) = f(t), u(0) = u_0$ 和 $u'(t) + A(t)B(t)u(t) + P(t)u(t) = f (t), u(0) = u_0$ 的最大正则问题。在这两种情况下，时间相关算子 $A(t)$ 与一系列倍半线性形式相关联，乘法左或右扰动 $B(t)$ 以及加性扰动 $P(t)$ 是所考虑的希尔伯特空间上的有界算子族。我们在形式和扰动的最小正则性假设下证明了先前问题的解决方案的最大 $L_p$-正则性结果和其他正则性属性。
We consider the problem of maximal regularity for non-autonomous Cauchy problems $u'(t) + B(t)A(t)u(t) + P(t)u(t) = f(t), u(0) = u_0$ and $u'(t) + A(t)B(t)u(t) + P(t)u(t) = f (t), u(0) = u_0$. In both cases, the time dependent operators $A(t)$ are associated with a family of sesquilinear forms and the multiplicative left or right perturbations $B(t)$ as well as the additive perturbation $P(t)$ are families of bounded operators on the considered Hilbert space. We prove maximal $L_p$-regularity results and other regularity properties for the solutions of the previous problems under minimal regularity assumptions on the forms and perturbations.
J-L Lions 关于非自治形式控制方程的最大正则性问题
DOI：
10.1016/j.anihpc.2016.05.001
发表时间：
2017
期刊：
arXiv: Functional Analysis
影响因子：
--
作者：
S. Fackler
通讯作者：
S. Fackler