Stabilization of Statistical Solutions to the Wave Equation in the Even-Dimensional Space

Abstract:

Consider the wave equations in IR^{n} , 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 → ∞.

Publication language:russian,
pages:36

Research direction:

Mathematical problems and theory of numerical methods