Polynomial stability of operator semigroups

By András Bátkai, Klaus-Jochen Engel, Jan Prüss, Roland Schnaubelt. 2006

163 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8b4f022cbcc994b77301741f77f51db4add77575

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Tatjana Eisner
2. Yuri Tomilov
3. R. Chill
4. C. Batty
5. A. Borichev
6. Zhuangyi Liu
7. Thomas Duyckaerts
8. Ramón Quintanilla

In Control and Systems Engineering

1. Yuri Tomilov
2. C. Batty
3. Tatjana Eisner
4. R. Chill
5. Thomas Duyckaerts
6. A. Borichev
7. Jianghao Hao
8. Zhuangyi Liu

In Mathematical Physics

1. Yuri Tomilov
2. C. Batty
3. A. Borichev
4. Thomas Duyckaerts
5. Tatjana Eisner
6. R. Chill
7. Jianghao Hao
8. Zhuangyi Liu

Citations in the corpus

• Stability of an abstract system of coupled hyperbolic and parabolic equations (2012, result): “One year later, a similar result was obtained in [4].”
• Stability of Timoshenko systems with past history (2008, unknown): “Our main tools are Prüss’ results on the exponential stability of semigroups, see [7,8].”
• Optimal polynomial decay of functions and operator semigroups (2009, background): “oved by removing the logarithmic factor in (1.6) in the case when Xis a Hilbert space, and that this factor is necessary if Xis merely a Banach space, see [6, Remark 9]. (See also the introduction in [3] and the comments after Theorem 3.5 therein.) OPTIMAL POLYNOMIAL DECAY 3 In our paper, we address”
• Fine scales of decay of operator semigroups (2013, background): “ved in [18] and [52] to 1/log(3 +t). These results gave rise to a number of papers treating the rates of decay of solutions to PDEs by abstract semigroup methods. Among them, we would like to mention [9], [16], [19], [21], [22], [53], and especially the very recent paper [4] as samples. This last pa”
• Non-uniform stability for bounded semi-groups on Banach spaces (2008, methodology): “The previously known polynomial decay results are as follows: Theorem B (Bátkai-Engel-Prüss-Schnaubelt, Liu-Rao).”
• Stability of Operators and Operator Semigroups (2010, result): “As some recent contributions we mention papers by Batkai, Engel, Prüss, Schnaubelt [20], Batty, Duyckaerts [25] and Borichev, Tomilov [39] on polynomial decay of the orbits and Chill, Tomilov [49] on characterisations of strong stability on Banach spaces with Fourier type.”