The macrodynamics of open systems and the variational principle of the local potential—I

Abstract The first part of the paper presents a general phenomenological approach for macroscopic description of the dynamics of open systems far from the equilibrium state. A class of ordinary differential macrodynamic equations is introduced and theorems on existence, uniqueness and stability of stationary states are proved. Singularly perturbed macrodynamic equations are considered. The procedure of simplification for these equations is defined and a theorem on proximity of solutions of the initial and the simplified systems is proved. The variational principle of the local potential for macrodynamic equations is formulated and studied. Iterative procedures for computing stationary states based on this principle are constructed.