Coexistence of phases in final one-dimensional systems

Within the framework of L.D. Landau (1908-1968) approach it is shown, that two-phase equilibrium is possible in linear macrosystems of the final size at low temperatures. At further downturn of temperature two-phase equilibrium becomes unstable and the system passes in a single-phase state. These results remain in force and at the account of interaction of interphase borders with each other and with the ends of linear system. Following Landau [1] we shall consider the linear system made of alternating pieces of two various phases. Points of contact between various phases (interphase borders) we shall present as a weak solution. For linear system of the limited size\textit{ L (L$>>$} 1) at low temperatures a single-phase state is stable. The increase in temperature will lead to phase transition of the first order in a two-phase state. The original cascade of phase transitions of the first order, because of increase of quantity of interphase border \textit{of item } will be observed actually. 1. L.D.Landau, E.M.Lifshits. Theoretical physics. Statistical physics. A part 1. 4 edition. Moscow (In Russian): the Science publisher, 1995.