Optimal control problems with final observation governed by explosive parabolic equations

被引：6
|
作者：
Amann, H
Quittner, P
机构：
[1] Univ Zurich, Inst Math, CH-8057 Zurich, Switzerland
[2] Comenius Univ, Dept Appl Math & Stat, SK-84248 Bratislava, Slovakia
来源：
SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2005年 / 44卷 / 04期
关键词：
optimal control problem; nonlinear parabolic equation; blow-up; final observation; optimality conditions; strong nonlinearities;
D O I：
10.1137/S0363012903433450
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
We study optimal control problems with final observation. The governing parabolic equations or systems involve superlinear nonlinearities, and their solutions may blow up infinite time. Our proof of the existence, regularity, and optimality conditions for an optimal pair is based on uniform a priori estimates for the approximating solutions. Our conditions on the growth of the nonlinearity are essentially optimal. In particular, we also solve a long-standing open problem of Lions concerning singular systems.
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页码：1215 / 1238
页数：24
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