Characterization of polynomial decay rate for the solution of linear evolution equation

被引:247
作者
Liu, ZY [1 ]
Rao, BP
机构
[1] Univ Minnesota, Dept Math & Stat, Duluth, MN 55812 USA
[2] Univ Louis Pasteur Strasbourg 1, Inst Rech Math Avancee, F-67084 Strasbourg, France
来源
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2005年 / 56卷 / 04期
关键词
polynomial decay rate; frequency domain; semigroup;
D O I
10.1007/s00033-004-3073-4
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we study the decay rate of solutions to strongly stable, but not exponentially stable linear evolution equations. It is known that the resolvent operator of such an equation must be unbounded on the imaginary axis. Our main result is an estimate of the decay rate when the unboundedness is of polynomial order. We then apply our main theorem to three strongly stable but not exponentially stable systems to obtain the decay rate, which is not available in the literature.
引用
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页码:630 / 644
页数:15
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