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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2020, Volume 492, Pages 27–30
DOI: https://doi.org/10.31857/S2686954320030078 (Mi danma67) 		 
MATHEMATICS

On stationary nonequilibrium measures for wave equations

T. V. Dudnikova

Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow, Russian Federation
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DOI: https://doi.org/10.31857/S2686954320030078
Abstract: In the paper, the Cauchy problem for wave equations with constant and variable coefficients is considered. We assume that the initial data are a random function with finite mean energy density and study the convergence of distributions of the solutions to a limiting Gaussian measure for large times. We derive the formulas for the limiting energy current density (in mean) and find a new class of stationary nonequilibrium states for the studied model.
Keywords: wave equations, random initial data, mixing condition, weak convergence of measures, Gaussian and Gibbs measures, energy current density, nonequilibrium states.
Presented: B. N. Chetverushkin
Received: 05.03.2020
Revised: 05.03.2020
Accepted: 23.03.2020
English version:
Doklady Mathematics, 2020, Volume 101, Issue 3, Pages 195–197
DOI: https://doi.org/10.1134/S1064562420030072
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: T. V. Dudnikova, “On stationary nonequilibrium measures for wave equations”, Dokl. RAN. Math. Inf. Proc. Upr., 492 (2020), 27–30; Dokl. Math., 101:3 (2020), 195–197
Citation in format AMSBIB
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\by T.~V.~Dudnikova
\paper On stationary nonequilibrium measures for wave equations
\jour Dokl. RAN. Math. Inf. Proc. Upr.
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\vol 492
\pages 27--30
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\crossref{https://doi.org/10.31857/S2686954320030078}
\zmath{https://zbmath.org/?q=an:7424587}
\elib{https://elibrary.ru/item.asp?id=42929990}
\transl
\jour Dokl. Math.
\yr 2020
\vol 101
\issue 3
\pages 195--197
\crossref{https://doi.org/10.1134/S1064562420030072}
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