A Remark on Null Exact Controllability of the Heat Equation

2001 ◽  
Vol 40 (1) ◽  
pp. 39-53 ◽  
Author(s):  
Xu Zhang
Keyword(s):  
Heat Equation ◽  
Exact Controllability

scholarly journals Exact Controllability of the Heat Equation by Temporarily Strategic Actuators Borders

2019 ◽  
Vol 11 (6) ◽  
pp. 53
Author(s):  
Cheikh SECK
Keyword(s):  
Heat Equation ◽  
Exact Controllability ◽  
Internal Controls ◽  
Time Variable ◽  
Parabolic Operator

The use of the strategic zone actuators, where possible, to control a system is simpler because the unknown functions depend only on the time variable. However, the restrictions and difficulties for establishing the coercivity inequality of the parabolic operator, requires looking for other methods of internal controls. So, we will generalize the concept of actuators strategic areas and deduce results of exact controllability.

Resolving controls for exact and approximate controllability of viscous Burgers’ equation: The Green’s function approach

2018 ◽  
Vol 29 (06) ◽  
pp. 1850045 ◽  
Author(s):  
Asatur Zh. Khurshudyan
Keyword(s):  
Heat Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Approximate Controllability ◽  
Burgers Equation ◽  
Sufficient Conditions ◽  
Exact Controllability ◽  
Function Approach ◽  
Dimensional System ◽  
Linear Algebraic Equations

In this paper, we consider a nonlinear control problem for one-dimensional viscous Burgers’ equation associated with a controlled linear heat equation by means of the Hopf–Cole transformation. The control is carried out by the time-dependent intensity of a distributed heat source influencing the heat equation. The set of admissible controls consists of compactly supported [Formula: see text] functions. Using the Green’s function approach, we analyze the possibilities of exact and approximate establishment of a given terminal state for the associated nonlinear Burgers’ equation within a desired amount of time. It is shown that the exact controllability of the associated Burgers’ equation and the heat equation are equivalent. Furthermore, sufficient conditions for the approximate controllability are derived. The set of resolving controls is constructed in both cases. The determination of the resolving controls providing exact controllability is reduced to an infinite-dimensional system of linear algebraic equations. By means of the heuristic method of resolving control determination, parametric hierarchies of solutions providing approximate controllability are constructed. The results of a numerical simulation supporting the theoretical derivations are discussed.

scholarly journals Exact controllability to the trajectories of the heat equation with Fourier boundary conditions: the semilinear case

2006 ◽  
Vol 12 (3) ◽  
pp. 466-483 ◽  
Author(s):  
Enrique Fernández-Cara ◽  
Manuel González-Burgos ◽  
Sergio Guerrero ◽  
Jean-Pierre Puel
Keyword(s):  
Boundary Conditions ◽  
Heat Equation ◽  
Exact Controllability

scholarly journals On the exact controllability of a nonlinear stochastic heat equation

2006 ◽  
Vol 2006 ◽  
pp. 1-12
Author(s):  
Bui An Ton
Keyword(s):  
Boundary Conditions ◽  
Heat Equation ◽  
Dirichlet Boundary ◽  
Exact Controllability ◽  
Stochastic Heat Equation ◽  
Dirichlet Boundary Conditions ◽  
Target Values

The exact controllability of a nonlinear stochastic heat equation with null Dirichlet boundary conditions, nonzero initial and target values, and an interior control is established.

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