The Liouville operator (Q1190933)

A Hamiltonian dynamical system in a domain with piecewise smooth boundary (reflections of trajectories are absolutely elastic) is considered. The full description of the infinitesimal operator \(A\) of the group \(I_ t\) of isometric operators defined by the trajectories is given; in particular, there is the description of the class of initial data for which the Liouville equation, \(\partial u/\partial t=-Au\), is strongly solvable.