scholarly journals Null-controllability and control cost estimates for the heat equation on unbounded and large bounded domains

2020 ◽  
pp. 117-157 ◽  
Author(s):  
Michela Egidi ◽  
Ivica Nakić ◽  
Albrecht Seelmann ◽  
Matthias Täufer ◽  
Martin Tautenhahn ◽  
...  
Keyword(s):  
Heat Equation ◽  
Null Controllability ◽  
Bounded Domains ◽  
Control Cost ◽  
Cost Estimates ◽  
And Control

scholarly journals Null controllability of a nonlinear heat equation

2002 ◽  
Vol 7 (7) ◽  
pp. 375-383 ◽  
Author(s):  
G. Aniculăesei ◽  
S. Aniţa
Keyword(s):  
Heat Equation ◽  
Dirichlet Boundary ◽  
Null Controllability ◽  
Carleman Estimates ◽  
Nonlinear Heat Equation ◽  
Homogeneous Dirichlet Boundary Condition ◽  
Linearized System ◽  
Kakutani Fixed Point ◽  
Exact Null Controllability ◽  
Kakutani Fixed Point Theorem

We study the internal exact null controllability of a nonlinear heat equation with homogeneous Dirichlet boundary condition. The method used combines the Kakutani fixed-point theorem and the Carleman estimates for the backward adjoint linearized system. The result extends to the case of boundary control.

scholarly journals Null controllability of the heat equation in pseudo-cylinders by an internal control

2020 ◽  
Vol 26 ◽  
pp. 122
Author(s):  
Jon Asier Bárcena-Petisco
Keyword(s):  
Heat Equation ◽  
Internal Control ◽  
Cylindrical Part ◽  
Null Controllability ◽  
Carleman Estimate ◽  
Main Difficulty ◽  
Absorption Properties ◽  
Weighted Function ◽  
Cylindrical Structure ◽  
Linear Heat

In this paper we prove the null controllability of the heat equation in domains with a cylindrical part and limited by a Lipschitz graph. The proof consists mainly on getting a Carleman estimate which presents the usual absorption properties. The main difficulty we face is the loss of existence of the usual weighted function in C2 smooth domains. In order to deal with this, we use its cylindrical structure and approximate the system by the same system stated in regular domains. Finally, we show some applications like the controllability of the semi-linear heat equation in those domains.

Analysis on Factors to Cause the Price Change of Building Materials

2013 ◽  
Vol 683 ◽  
pp. 668-671 ◽  
Author(s):  
Huan Zhou ◽  
Jian Huan Zhao
Keyword(s):  
Building Materials ◽  
Investment Decision ◽  
Price Change ◽  
Market Price ◽  
Price Theory ◽  
Control Cost ◽  
Control Engineering ◽  
Bid Price ◽  
Engineering Cost ◽  
And Control

Building material cost accounts for about 65% of the engineering cost, and some even reach more than 75% in the current formation of the construction installation engineering cost in our country, so the price of materials determines the engineering cost to a great extent. It is essential for proprietor to master the price fluctuations of building materials to control engineering cost, and it is also important for contractor to determine the bid price. According to the market price theory and the basic characteristic of the building materials, this paper analyses and summarizes the influencing factors of building materials price changes, and provides some reference basis for the parties of building to give a investment decision and control cost.

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