A DETERMINISTIC OPTIMAL DESIGN PROBLEM FOR THE HEAT EQUATION

被引：5

作者：

Gimperlein, Heiko ^{[1
,2
,3
]}

Waters, Alden ^{[4
]}

机构：

[1] Heriot Watt Univ, Maxwell Inst Math Sci, Edinburgh EH14 4AS, Midlothian, Scotland

[2] Heriot Watt Univ, Dept Math, Edinburgh EH14 4AS, Midlothian, Scotland

[3] Univ Paderborn, Inst Math, Warburger Str 100, D-33098 Paderborn, Germany

[4] UCL, Dept Math, Gower St, London WC1E 6BT, England

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2017年 / 55卷 / 01期

基金：

英国工程与自然科学研究理事会;

关键词：

observability estimate; heat equation; optimal design; PARAMETRIX CONSTRUCTION; EXACT CONTROLLABILITY; WAVE-EQUATION; COEFFICIENTS;

D O I：

10.1137/15M1031084

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

For the heat equation on a bounded subdomain Omega of R-d, we investigate the optimal shape and location of the observation domain in observability inequalities. A new decomposition of L-2 (R-d) into heat packets allows us to remove the randomization procedure and assumptions on the geometry of Omega in previous works. The explicit nature of the heat packets gives new information about the observability constant in the inverse problem.

引用

页码：51 / 69

页数：19

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