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 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.

Mathematical problems and theory of numerical methods