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KIAM Preprint  77, Moscow, 2005
Authors: Dudnikova T.V.
On Convergence to Equilibrium for Wave Equations in IRn, with Odd n≥ 3.
Consider the wave equations in IRn, with n≥ 3 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 xn→ ∞, with the distributions m. We study the distribution mt of the random solution at a time t∈ IR. The main result is the convergence of mt to a Gaussian measure as t→ ∞ that means a central limit theorem for the wave equations. The application to the case of the Gibbs measures m=g with two different temperatures T is given.
Publication language: russian,  pages: 32
Research direction:
Mathematical problems and theory of numerical methods
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  • Dudnikova T.V.