Polynomial stability of operator semigroups

被引：115

作者：

Batkai, Andras

Engel, Klaus-Jochen

Pruess, Jan

Schnaubelt, Roland

机构：

[1] Univ Karlsruhe, Inst Anal, Dept Math, D-76128 Karlsruhe, Germany

[2] Univ Halle Wittenberg, Fb Math & Informat, D-06099 Halle, Germany

[3] Univ Aquila, Dipartimento Matemat, Sez Ingn, I-67040 Roio Poggio, Italy

[4] ELTE TTK, Dept Appl Anal, H-1518 Budapest, Hungary

来源：

MATHEMATISCHE NACHRICHTEN | 2006年 / 279卷 / 13-14期

关键词：

asymptotic behaviour; polynomial stability; C-0-semigroups; spectrum; Laplace transform; normal operators; coupled wave equation;

D O I：

10.1002/mana.200410429

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate polynomial decay of classical solutions of linear evolution equations. For bounded strongly continuous semigroups on a Banach space this property is closely related to polynomial growth estimates of the resolvent of the generator. For systems of commuting normal operators polynomial decay is characterized in terms of the location of the generator spectrum. The results are applied to systems of coupled wave-type equations. (C) 2006 WILEYNCH Verlag GmbH & Co. KGaA, Weinheim.

引用

页码：1425 / 1440

页数：16

共 16 条

[1] Indirect internal stabilization of weakly coupled evolution equations
Alabau, F
Cannarsa, P
Komornik, V
[J]. JOURNAL OF EVOLUTION EQUATIONS, 2002, 2 (02) : 127 - 150
[2] Indirect boundary stabilization of weakly coupled hyperbolic systems
Alabau-Boussouira, F
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2002, 41 (02) : 511 - 541
[3] [Anonymous], 1999, GRADUATE TEXTS MATH
[4] [Anonymous], 1985, OPERATOR THEORY
[5] Arendt W., 2001, MONOGRAPHS MATH, V96
[6] Dunford N., 1963, LINEAR OPERATORS PAR
[7] ENGEL KJ, UNPUB OPERATOR MATRI
[8] KREISS HO, 1959, MATH SCAND, V7, P71
[9] Latushkin Y, 2001, OPER THEOR, V129, P341
[10] Decay rates for the three-dimensional linear system of thermoelasticity
Lebeau, G
Zuazua, E
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1999, 148 (03) : 179 - 231

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