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
Mathematical problems and theory of numerical methods