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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2024, Volume 327, Pages 87–105
DOI: https://doi.org/10.4213/tm4431 (Mi tm4431) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Strict Lyapunov Functions and Energy Decay in Hamiltonian Chains with Degenerate Damping

Andrey V. Dymovab, Lev V. Lokutsievskiya, Andrey V. Sarychevc

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
b National Research University Higher School of Economics, Moscow, Russia
c Dipartimento di Matematica e Informatica U. Dini, Università degli Studi di Firenze, Florence, Italy
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DOI: https://doi.org/10.4213/tm4431
Abstract: We consider a Hamiltonian chain of rotators (in general nonlinear) in which the first rotator is damped. Being motivated by problems of nonequilibrium statistical mechanics of crystals, we construct a strict Lyapunov function that allows us to find a lower bound for the total energy dissipation rate when the energy and time are large. Our construction is explicit and its analysis is rather straightforward. We rely on a method going back to Matrosov, Malisoff, and Mazenc, which we review in our paper. The method is rather universal, and we show that it is applicable to a chain of oscillators as well.
Keywords: strict Lyapunov function, chain of oscillators, chain of rotators, mixing, degenerate dissipation, energy decay.
Funding agency Grant number
Russian Science Foundation 19-71-30012
The work of A. V. Dymov (Sections 1, 3, 5) was supported by the Russian Science Foundation under grant no. 19-71-30012, https://rscf.ru/en/project/19-71-30012/, and performed at the Steklov Mathematical Institute of Russian Academy of Sciences. All results in this paper are products of the authors' collaborative work.
Received: May 10, 2024
Revised: October 4, 2024
Accepted: October 7, 2024
Published: 12.03.2025
English version:
Proceedings of the Steklov Institute of Mathematics, 2024, Volume 327, Pages 78–95
DOI: https://doi.org/10.1134/S0081543824060075
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Andrey V. Dymov, Lev V. Lokutsievskiy, Andrey V. Sarychev, “Strict Lyapunov Functions and Energy Decay in Hamiltonian Chains with Degenerate Damping”, Mathematical Aspects of Mechanics, Collected papers. Dedicated to Dmitry Valerevich Treschev on the occasion of his 60th birthday and to Sergey Vladimirovich Bolotin on the occasion of his 70th birthday, Trudy Mat. Inst. Steklova, 327, Steklov Math. Inst., Moscow, 2024, 87–105; Proc. Steklov Inst. Math., 327 (2024), 78–95
Citation in format AMSBIB
\Bibitem{DymLokSar24}
\by Andrey~V.~Dymov, Lev~V.~Lokutsievskiy, Andrey~V.~Sarychev
\paper Strict Lyapunov Functions and Energy Decay in Hamiltonian Chains with Degenerate Damping
\inbook Mathematical Aspects of Mechanics
\bookinfo Collected papers. Dedicated to Dmitry Valerevich Treschev on the occasion of his 60th birthday and to Sergey Vladimirovich Bolotin on the occasion of his 70th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2024
\vol 327
\pages 87--105
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4431}
\crossref{https://doi.org/10.4213/tm4431}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=4884836}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2024
\vol 327
\pages 78--95
\crossref{https://doi.org/10.1134/S0081543824060075}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-105001511577}
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    • This publication is cited in the following 2 articles:
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
     
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