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.

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 Evolution equations with dynamic boundary conditions

1989 ◽  
Vol 113 (1-2) ◽  
pp. 43-60 ◽  
Author(s):  
Thomas Hintermann
Keyword(s):  
Boundary Conditions ◽  
Evolution Equations ◽  
Hyperbolic Equations ◽  
Cauchy Problems ◽  
Dynamic Boundary Conditions ◽  
Boundary Problems ◽  
Dynamic Boundary ◽  
Boundary Operators ◽  
Quasilinear Problems ◽  
Abstract Cauchy Problems

SynopsisIn this paper, we study boundary problems with dynamic boundary conditions, that is, with boundary operators containing time derivatives. The equations under consideration are transformed into abstract Cauchy problems x – Cx = f and x(0) = x0. Abstract theoretical results concerning the operators C are obtained by the study of a naturally arising pseudodifferential operator. For existence and uniqueness theorems concerning solutions of parabolic and hyperbolic equations, we then apply the theory of semigroups in Banach spaces. Some examples of semilinear and quasilinear problems, to which our results apply, are given.

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