论文标题
最大$ l^p $ - 用于抽象演化方程，并应用于闭环边界反馈控制问题
Maximal $L^p$-regularity for an abstract evolution equation with applications to closed-loop boundary feedback control problems
论文作者
论文摘要
在本文中，我们提出了一个抽象的最大$ l^p $ - 定期结果，最高$ t = \ infty $，它被调整为捕获抛物线类型的（线性）偏微分方程，该方程定义在有限的尺寸和有限的尺寸稳定性，稳定性，反馈控件（部分）上（一部分）。插图还包括一个更古典的边界抛物线示例外，还有两个最近的设置：（i）$ 3D $ -NAVIER-Stokes方程，具有有限的尺寸，局部，边界切向切向反馈稳定控制以及具有有限尺寸，本地化，反馈，稳定性的有限尺寸，稳定性的BousSinesQ系统，用于热力控制，用于热力控制。
In this paper we present an abstract maximal $L^p$-regularity result up to $T = \infty$, that is tuned to capture (linear) Partial Differential Equations of parabolic type, defined on a bounded domain and subject to finite dimensional, stabilizing, feedback controls acting on (a portion of) the boundary. Illustrations include, beside a more classical boundary parabolic example, two more recent settings: (i) the $3d$-Navier-Stokes equations with finite dimensional, localized, boundary tangential feedback stabilizing controls as well as Boussinesq systems with finite dimensional, localized, feedback, stabilizing, Dirichlet boundary control for the thermal equation.
