SOLUTIONS OF CONSERVATION LAW SYSTEMS

Abstract

The work covers the mathematical models of the physical systems described by the differential equations expressing the conservation properties. The aim is to reveal and analyse the basic mathematical structures connected with the problems of approximated method convergence; to prove the theorems about global solvability of the Cauchy problem for the quasi-linear and semi-linear systems having application in the mathematical physics. The convergence of regular approximated methods to the functional solution of conservation laws at condition of the weak approximation and weak method stability has been substantiated. The possible classes of correctness have been described. The convergence of difference method to the functional solution for the Boltzmann type equations has been substantiated. The solvability on a whole has been proved, and the convergence of approximated methods for the general type non-linear conservation lay systems and for concrete models has been substantiated. The results are used in the Moscow State University, in the Physical-Energetical Institute, in the Institute of Nuclear Power Engineering, in the Institute of Hydrodynamics a.o. The application field: gas dynamics, physical kineticsAvailable from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio