On Convergence to Equilibrium for Wave Equations in IR^{n}, with Odd n≥ 3.

Abstract:

Consider the wave equations in IR^{n}, 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 x_{n}→ ±∞, with the distributions m_{±}. We study the distribution m_{t} of the random solution at a time t∈ IR. The main result is the convergence of m_{t} 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