Consider the wave equations in IRⁿ , with constant or variable coefficients for even n ≥ 4. 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 two distinct 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 → ∞.

Mathematical problems and theory of numerical methods