Dynamic Boundary Conditions and Boundary Control for the One-Dimensional Heat Equation

2004 ◽  
Vol 10 (2) ◽  
pp. 213-225 ◽  
Author(s):  
Michael Kumpf ◽  
Gregor Nickel
Keyword(s):  
Boundary Conditions ◽  
Heat Equation ◽  
Boundary Control ◽  
Dynamic Boundary Conditions ◽  
One Dimensional ◽  
Dynamic Boundary ◽  
The One

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 On a singular heat equation with dynamic boundary conditions

2016 ◽  
Vol 97 (1-2) ◽  
pp. 27-59 ◽  
Author(s):  
Giulio Schimperna ◽  
Antonio Segatti ◽  
Sergey Zelik
Keyword(s):  
Boundary Conditions ◽  
Heat Equation ◽  
Dynamic Boundary Conditions ◽  
Dynamic Boundary

scholarly journals Stackelberg-Nash null controllability of heat equation with general dynamic boundary conditions

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Idriss Boutaayamou ◽  
Lahcen Maniar ◽  
Omar Oukdach
Keyword(s):  
Boundary Conditions ◽  
Heat Equation ◽  
Hierarchical Control ◽  
Null Controllability ◽  
Carleman Estimates ◽  
Dynamic Boundary Conditions ◽  
Dynamic Boundary ◽  
Drift Terms ◽  
Controllability Result ◽  
General Dynamic

<p style='text-indent:20px;'>This paper deals with the hierarchical control of the anisotropic heat equation with dynamic boundary conditions and drift terms. We use the Stackelberg-Nash strategy with one leader and two followers. To each fixed leader, we find a Nash equilibrium corresponding to a bi-objective optimal control problem for the followers. Then, by some new Carleman estimates, we prove a null controllability result.</p>

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