Development of the actual state principle for a physical system

Introduction. The article briefly discusses the state of scientific research in the field of mathematical modeling of physical systems with distributed parameters. Mathematical modeling in elasticity theory. The initial boundary value problem of linear elasticity theory is formulated. It is shown that using measured and unmeasured variables, it is possible to construct a positive definite energy relationship, which allows not only to use the variational technique to find an approximate solution, but also to design objective estimates of its quality. Two-dimensional problem of elasticity theory (static case). Using the example of solving a two-dimensional static problem of linear elasticity, the advantages of the proposed approach are discussed in detail. Mathematical modeling in fluid theory. The variational principle in fluid theory is formulated. Optimal pressure control. Using the example of solving the problem of the motion control for ideal and viscous fluids in pipeline systems, the issues of finding an approximate solution and estimating its accuracy are discussed. Energy principle in the heat transfer problem. The variational principle in the linear heat transfer problem is formulated. Two-dimensional heat transfer problem. The features of constructing a solution to a control problem in a two-dimensional heat transfer theory are discussed in detail. Generalizing principle. A generalizing principle of the actual state of a physical system is formulated, which can be effectively applied for a detailed description and analysis of physical processes.