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. 
@article{DANMA_2020_492_a5,
     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},
     publisher = {mathdoc},
     volume = {492},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2020_492_a5/}
}
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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/