The controllability of the Gurtin-Pipkin equation: A cosine operator approach

被引：60
作者：
Pandolfi, L [1 ]
机构：
[1] Politecn Torino, Dipartimento Matemat, I-10129 Turin, Italy
来源：
APPLIED MATHEMATICS AND OPTIMIZATION | 2005年 / 52卷 / 02期
关键词：
heat equation with memory; exacty controllability; cosine operators;
D O I：
10.1007/s00245-005-0819-0
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we give a semigroup-based definition of the solution of the Gurtin-Pipkin equation with Dirichlet boundary conditions. It turns out that the dominant term of the input-to-state map is the control to displacement operator of the wave equation. This operator is surjective if the time interval is long enough. We use this observation in order to prove exact controllability in finite time of the Gurtin-Pipkin equation.
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页码：143 / 165
页数：23
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