THEORETICAL SOLUTION OF THE PROTECTION OF PEOPLE FROM THE DAMAGING FACTORS OF THE RADIOACTIVE AND THE CHEMICAL POLLUTION OF THE ATMOSPHERE

Abstract

The paper provides a theoretical solution to the problem of developing a mathematical model for protecting people from the damaging factors of radioactive and chemical pollution of the atmosphere in temporary shelters in open areas that can occur during technogenic accidents at protected critical infrastructure sites. It reduces to the problem of air injection in a local volume and the movement of air flow in a local volume. These problems belong to the class of boundary problems of mathematical physics, which are solved by the method of expansion in non-orthogonal functions. To do this, we take a multidimensional multiply connected domain bounded by a multilayer surface and a system of vector functions, each of which is linearly independent and complete in the space under consideration and square integrable vector-functions on the used surface. Then we can consider an approximate solution of the problem, which tends to an exact solution under the condition that this problem is correct. In the case of incorrect boundary-value problems, a reasonable approximation is used to solve this problem. In other words, the solution of this boundary value problem is representable as the "simple layer potential" of the representation function, which can be expanded in a system of nonorthogonal functions with arbitrarily high accuracy. That is, the solution of the problem of air injection and air flow movement in a local volume is represented by a system of equations in which the first dependence describes the potential of a simple airflow layer formed during the air injection process into the local volume, the second shows the difference between the simple airflow density function and the matrix Its approximate integral representation, and the third describes the expansion coefficients determined by the accuracy of the solution of the problem.