Mathematical aspects of optimal control of transference processes in spatial networks

Abstract

Abstract The new kind of practical issues was born due to modern trend on globalization and transition to the concept of industry 4.0. These are the processes in commercial networks representing the movement of goods and finance, which have specific economic indicators; migration of populations and labor resources; transference of one-parameter continuous media (diffusion effect). The issues with higher level of complexity occur during the research of multi-phase environments dynamics in network-like media and mathematical modeling of such processes. The authors divide these two problems and offer the formalized description for the laminar processes and dynamic convective processes with feedback. There was developed an approach to solve the problems of optimal control for these processes. The research is based on methods for analyzing systems of partial differential equations with distributed parameters on a graph or network-like domain.