The aim of this chapter is to introduce the concept of regional boundary exponential reduced observability in connection with the sensors characterizations on a sub-region on boundary of the considered domain boundary. More precisely, we explore the original results devoted to this concept in linear dynamical systems which is generated by a strongly continuous semi-group in Hilbert space of order one. Thus, the existence of sufficient conditions is presented and examined for regional boundary exponential reduced estimator in parabolic infinite dimensional systems. Finally, we apply these results to the exchange systems with various strategic sensors.
The Regional Boundary Reconstruction Problem of the Initial State for Fractional Semilinear Systems
Ibnou Zohr University（伊本·佐哈尔大学）；The Higher School of Education and Training（高等教育与培训高等学院）；Moulay Ismail University（穆莱·伊斯梅尔大学）；Faculty of Sciences（理学院）；University of Aveiro（阿威罗大学）；Center for Research and Development in Mathematics and Applications (CIDMA)（数学与应用研究与发展中心）
Feedback stabilization of linear and bilinear unbounded systems in Banach space
我们考虑$\dot{y}(t)=Ay(t)-μB C y(t)$形式的线性控制系统，其中$μ$是正实参数，$A$是状态算子，并在巴拿赫空间上生成压缩线性$C_0-$半群$S(t) $。$X$、$B$和$C$分别是控制和可观测性算子，它们被定义在适当的空间中，在某种意义上它们是无界的。我们的目的是证明上述系统的指数稳定性的充分条件表示的容许性和可观性。还考虑了双线性控制的一致指数镇定问题。还提供了输运和热方程的应用。
Revisiting the Direct Fourier Filtering Technique for the Maximal Decay Rate of Boundary-damped Wave Equation by Finite Differences and Finite Elements
