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Preprints of the Keldysh Institute of Applied Mathematics, 2005, 077, 32 pp.
(Mi ipmp718)
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On convergence to equilibrium for wave equations in $\mathbb R^n$, with odd $n\ge3$
T. V. Dudnikova
Abstract:
Consider the wave equations in $\mathbb R^n$, with $n\ge3$ and odd, with constant or variable coefficients. The initial datum is a random function with a finite mean density of energy that satisfies a Rosenblatt- or Ibragimov-Linnik-type mixing condition. It is assumed that the initial random function converges to different space-homogeneous processes as $x_n\to\pm\infty$, with the distributions $\mu_\pm$. We study the distribution $\mu_t$ of the random solution at a time $t\in\mathbb R$. The main result is the convergence of $\mu_t$ to a Gaussian measure as $t\to\infty$ that means a central limit theorem for the wave equations. The application to the case of the Gibbs measures $\mu_\pm=g_\pm$ with two different temperatures $T_\pm$ is given.
Citation:
T. V. Dudnikova, “On convergence to equilibrium for wave equations in $\mathbb R^n$, with odd $n\ge3$”, Keldysh Institute preprints, 2005, 077, 32 pp.
Linking options:
https://www.mathnet.ru/eng/ipmp718 https://www.mathnet.ru/eng/ipmp/y2005/p77
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Statistics & downloads: |
Abstract page: | 69 | Full-text PDF : | 37 |
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