scholarly journals A boundary control problem for the pure Cahn–Hilliard equation with dynamic boundary conditions

2015 ◽  
Vol 4 (4) ◽  
pp. 311-325 ◽  
Author(s):  
Pierluigi Colli ◽  
Gianni Gilardi ◽  
Jürgen Sprekels
Keyword(s):  
Boundary Conditions ◽  
Control Problem ◽  
Boundary Control ◽  
Necessary Conditions ◽  
Dynamic Boundary Conditions ◽  
First Order ◽  
Boundary Control Problem ◽  
Dynamic Boundary ◽  
Necessary Conditions For Optimality ◽  
Cahn Hilliard Equation

AbstractA boundary control problem for the pure Cahn–Hilliard equations with possibly singular potentials and dynamic boundary conditions is studied and first-order necessary conditions for optimality are proved.

scholarly journals Optimal boundary control of distributed systems involving dynamic boundary conditions

1998 ◽  
Vol 3 (5) ◽  
pp. 387-411
Author(s):  
S. Kerbal ◽  
N. U. Ahmed
Keyword(s):  
Heat Transfer ◽  
Distributed Systems ◽  
Boundary Conditions ◽  
Control Problem ◽  
Necessary Conditions ◽  
Transfer Problem ◽  
Optimal Controls ◽  
Dynamic Boundary Conditions ◽  
Dynamic Boundary ◽  
Boundary Operators

In this paper we consider Lagrange type control problem for systems involving dynamic boundary conditions that is, with boundary operators containing time derivatives. Assuming the existence of optimal controls,B-evolutions theory is used to present necessary conditions of optimality. The result is illustrated by an example from heat transfer problem and also an algorithm for computing optimal controls is presented.

The problem of boundary control of string vibrationsby displacement of the left end when the right end is fixedwith the given values of the deflection functionat intermediate times

2020 ◽  
pp. 131-146
Author(s):  
Vanya R. Barseghyan ◽  
Svetlana V. Solodusha
Keyword(s):  
Boundary Conditions ◽  
Control Problem ◽  
Boundary Control ◽  
Constructive Method ◽  
Boundary Control Problem ◽  
String Vibrations ◽  
Classical Boundary ◽  
The Right ◽  
The Given

We consider the boundary control problem for the homogeneous string vibrationequation with given the classical boundary (initial and final) conditions and with given valuesof the deflection function at intermediate times. The control is performed by displacementof the left end of the string when the right end is fixed. The problem is reduced to thecontrol problem with zero boundary conditions. We propose the constructive method forconstructing the boundary control of the process of string vibrations with given values ofthe deflection function at intermediate times.We present the results of numerical experimentsand the corresponding graphs confirm the validity of the results.

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