On Regional Boundary Gradient Strategic Sensors In Diffusion Systems

This paper is aimed at investigating and introducing the main results regarding the concept of Regional Boundary Gradient Strategic Sensors (RBGS-sensors the in Diffusion Distributed Parameter Systems (DDP-Systems . Hence, such a method is characterized by Parabolic Differential Equations (PDEs in which the behavior of the dynamic is created by a Semigroup ( of Strongly Continuous type (SCSG in a Hilbert Space (HS) . Additionally , the grantee conditions which ensure the description for such sensors are given respectively to together with the Regional Boundary Gradient Observability (RBG-Observability can be studied and achieved . Finally , the results gotten are applied to different situations with altered sensors positions are undertaken and examined.

An overdetermined problem for the infinity-Laplacian around a set of positive reach

We consider an overdetermined problem associated to an inhomogeneous infinity-Laplace equation. More precisely, the domain of the problem is required to contain a given compact set K of positive reach, and the boundary of the domain must lie within the reach of K. We look for a solution vanishing at the boundary and such that the outer derivative depends only on the distance from K. We prove that if the boundary gradient grows fast enough with respect to such distance (faster than the distance raised to {\frac{1}{3}} ), then the problem is solvable if and only if the domain is a tubular neighborhood of K, thus extending a previous result valid in the case when K is made up of a single point.

Regional Boundary Gradient Detectability in Distributed Parameter Systems

The aim of this paper is study and explore the notion of the regional boundary gradient detectability in connection with the choice of strategic gradient sensors on sub-region of the considered system domain boundary. More precisely, the principal reason behind introducing this notion is that the possibility to design a dynamic system (may be called regional boundary gradient observer) which enable to estimate the unknown system state gradient. Then for linear infinite dimensional systems in a Hilbert space, we give various new results related with different measurements. In addition, we provided a description of the regional boundary exponential gradient strategic sensors for completion the regional boundary exponential gradient observability and regional boundary exponential gradient detectability. Finally, we present and illustrate the some applications of sensors structures which relate by regional boundary exponential gradient detectability in diffusion distributed parameter systems.