an:03884006
Zbl 0554.93004
Orlov, V. N.; Rozonoer, L. I.
The macrodynamics of open systems and the variational principle of the local potential. I
EN
J. Franklin Inst. 318, 283-314 (1984).
00149400
1984
j
93A10 49S05 80A30 34D15 37-XX 92Cxx 82B35
open systems; macrodynamic equations; stationary states; simplification; variational principle of the local potential
The first part of this paper, which consists of two parts, presents a general phenomenological approach for a macroscopic description of the dynamics of open systems far from the equilibrium state. A class of ordinary differential macrodynamic equations is introduced and theorems of 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. The second part of the paper is devoted to applications.
M.Rijckaert