Geodesic
On stationary nonequilibrium measures for wave equations
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 492 (2020), pp. 27-30

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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. 
T. V. Dudnikova. On stationary nonequilibrium measures for wave equations. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 492 (2020), pp. 27-30. http://geodesic.mathdoc.fr/item/DANMA_2020_492_a5/
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     author = {T. V. Dudnikova},
     title = {On stationary nonequilibrium measures for wave equations},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {27--30},
     year = {2020},
     volume = {492},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2020_492_a5/}
}
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