Composition of the packed block elements into the block structure and their homeomorphisms

Abstract

Currently, the problem of building block elements of boundary problems for systems of differential equations with constant coefficients has been solved for a fairly wide range of domains. For the formation of block structures consisting of block elements with individual physical and mechanical properties, the mechanism of their conjugation is used, which is, in terms of topology, the construction of quotient topologies of topological spaces of conjugated block elements. This mechanism is described using the example of packed block elements generated by the boundary value problem for systems of linear differential equations in partial derivatives viewed as topological objects. They can be considered as manifolds with boundaries in certain spaces representing Cartesian products of topological spaces. Thus, the packed block elements are conjugated to form block structures of varying complexity. This approach is based on the methods of exterior analysis, the section of the theory of block elements, which makes it possible to build solutions of boundary problems on given carriers. The paper discusses other approaches to the application of topological methods in boundary value problems. Clear goals, approaches and opportunities of different methods are described.