OPTIMAL CONTROL FOR THE THERMISTOR PROBLEM

被引：29
|
作者：
Hoemberg, D. [1 ]
Meyer, C. [1 ]
Rehberg, J. [1 ]
Ring, W. [2 ]
机构：
[1] Weierstrass Inst Appl Anal & Stochast, D-10117 Berlin, Germany
[2] Graz Univ, Inst Math, A-8010 Graz, Austria
来源：
SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2010年 / 48卷 / 05期
基金：
奥地利科学基金会;
关键词：
partial differential equations; optimal control problems; state constraints; SEMILINEAR ELLIPTIC-EQUATIONS; 2ND-ORDER;
D O I：
10.1137/080736259
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
This paper is concerned with the state-constrained optimal control of the two-dimensional thermistor problem, a quasi-linear coupled system of a parabolic and elliptic PDE with mixed boundary conditions. This system models the heating of a conducting material by means of direct current. Existence, uniqueness, and continuity for the state system are derived by employing maximal elliptic and parabolic regularity. By similar arguments the linearized state system is discussed, while the adjoint system involving measures is investigated using a duality argument. These results allow us to derive first-order necessary conditions for the optimal control problem.
引用
收藏
页码：3449 / 3481
页数：33
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