Stabilization of Statistical Solutions to the Wave Equation in the Even-Dimensional Space
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 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 → ∞.
Mathematical problems and theory of numerical methods