Generalization of the Landau-Vlasov kinetic equation for a dissipative randomly driven system

The Landau-Vlasov kinetic equation is generalized for dissipative randomly driven systems. The work is a development of the paper by Sliusarenko, Chechkin, and Slyusarenko (J. Math. Phys., 56, 043302, 2015) and is based on the Bogolyubov reduced description method. The kinetic equation is obtained up to the second order in small potential and dissipative interactions and small correlation functions of an external random field. The evolution of a spatially homogenous system is investigated for a simple model on the basis of the obtained kinetic equation. A temperature time equation is derived, and a steady state of the system is investigated.