Stabilization of statistical solutions of the Klein-Gordon equation (Q1819288)

The author defines the so-called 'statistical solution' to the Klein- Gordon equation \[ \partial^ 2u/\partial t^ 2(t,x)-(c^ 2\Delta - m^ 2)u(t,x)=0,\quad t>0,\quad x\in {\mathbb{R}}^ n; \] \[ u(0,x)=u^ 0(x),\quad \partial u/\partial t(0,x)=u^ 1(x),\quad x\in {\mathbb{R}}^ n, \] and proves that this solution converges to the homogeneous Gauss measure as \(t\to +\infty\) if the initial data satisfy some energy estimates.