Semi-uniform stability of operator semigroups and energy decay of damped waves

被引：18

作者：

Chill, R. ^{[1
]}

Seifert, D. ^{[2
]}

Tomilov, Y. ^{[3
]}

机构：

[1] Tech Univ Dresden, Inst Anal, Fak Math, D-01062 Dresden, Germany

[2] Newcastle Univ, Sch Math Stat & Phys, Newcastle Upon Tyne NE1 7RU, Tyne & Wear, England

[3] Polish Acad Sci, Inst Math, Sniadeckich 8, PL-00956 Warsaw, Poland

来源：

PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2020年 / 378卷 / 2185期

关键词：

operator semigroups; semi-uniform stability; damped wave equation; SPECTRAL MAPPING-THEOREM; TAUBERIAN-THEOREMS; GEOMETRIC CONTROL; EXACT CONTROLLABILITY; ASYMPTOTIC-BEHAVIOR; EXPONENTIAL DECAY; VALUED FOURIER; L-P; EQUATION; RATES;

D O I：

10.1098/rsta.2019.0614

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

Only in the last 15 years or so has the notion of semi-uniform stability, which lies between exponential stability and strong stability, become part of the asymptotic theory ofC(0)-semigroups. It now lies at the very heart of modern semigroup theory. After briefly reviewing the notions of exponential and strong stability, we present an overview of some of the best known (and often optimal) abstract results on semi-uniform stability. We go on to indicate briefly how these results can be applied to obtain (sometimes optimal) rates of energy decay for certain damped second-order Cauchy problems. This article is part of the theme issue 'Semigroup applications everywhere'.

引用

页数：24

共 13 条

[1] Semi-uniform input-to-state stability of infinite-dimensional systems
Wakaiki, Masashi
MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS, 2022, 34 (04) : 789 - 817
[2] Semi-uniform input-to-state stability of infinite-dimensional systems
Masashi Wakaiki
Mathematics of Control, Signals, and Systems, 2022, 34 : 789 - 817
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Xiao, Ti-Jun
SEMIGROUP FORUM, 2025, 110 (01) : 162 - 189
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Communications in Mathematical Physics, 2006, 268 : 481 - 504
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JOURNAL OF DIFFERENTIAL EQUATIONS, 2011, 251 (07) : 1841 - 1863
[8] Uniform exponential long time decay for the space semi-discretization of a locally damped wave equation via an artificial numerical viscosity
Tébou, LRT
Zuazua, E
NUMERISCHE MATHEMATIK, 2003, 95 (03) : 563 - 598
[9] Uniform exponential long time decay for the space semi-discretization of a locally damped wave equation via an artificial numerical viscosity
Louis Roder Tcheugoué Tébou
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Numerische Mathematik, 2003, 95 : 563 - 598
[10] A unified approach via convexity for optimal energy decay rates of finite and infinite dimensional vibrating damped systems with applications to semi-discretized vibrating damped systems
Alabau-Boussouira, Fatiha
JOURNAL OF DIFFERENTIAL EQUATIONS, 2010, 248 (06) : 1473 - 1517

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