STUDY OF THE CORRECTNESS CONDITIONS OF BOUNDARY VALUE PROBLEMS FOR MULTILAYER BIOTECHNOLOGICAL ENVIRONMENT

Abstract

The problem of rational use of energy and other resources is relevant in the context of uncertainty of the national economy. In order to improve the accuracy of diagnostics and control of simulated systems, the development of new high-precision software and hardware for technological and biotechnological processes is required. Carrying out mathematical simulation of the state of the studied object of atypical geometric shape and multi-layer structure it is impossible to guarantee the existence and uniqueness of the solution of the boundary value problem for differential equations. To model physical actions in complex systems, it is necessary to take into account the structure of the object under study and peculiarities of emitters when constructing boundary value problems with differential equations. However, this will increase the complexity of the implementation of boundary value problems. Correctness of boundary value problems leads to correctness of applied optimization mathematical models of problems of search for optimal parameters of action sources taking into account restrictions on target function and its parameters.

In the article the mathematical modeling of the process of laser action on the embryo is carried out. The author has defined and substantiated the conditions of correctness of the boundary value problems describing the state of the modeled biotechnological system under the action of focused laser radiation sources. The methods on the theory of pseudo-differential equations in the space of generalized functions of degree growth (incidence) have been used for substantiating the correctness of the boundary value problem. It is proved that the symbol of a pseudodifferential equation is the sum of exponentially correct and subordinate symbols of pseudodifferential operators. It is reasonable to use the technique proposed in the article to substantiate the correctness of nonlocal boundary value problems for differential equations describing the state of other technological and biotechnological systems and applied optimization mathematical models.