Asymptotics of the solution of non-stationary interface convection problem in thin layer of viscous liquid

The paper is concerned with non-stationary non-linear model problem of Marangony interface convection in thin plane layer of viscous non-compressible liquid. Asymptotic approximation of the solution with respect to a small parameter characterizing the thickness of the liquid layer is constructed. This paper continues the previous investigations where the stationary problem has been solved.