The cauchy problem for a nonlinear integro-differential transport equation

In the present paper, we study the Cauchy problem for a nonlinear time-dependent kinetic neutrino transport equation. We prove the existence and uniqueness theorem for the solution of the Cauchy problem, establish uniform bounds in $t$ for the solution of this problem, and prove the existence and uniqueness of a stationary trajectory and the stabilization as $t\to\infty$ of the solution of the time-dependent problem for arbitrary initial data.