Abstract
Globalization has given a powerful impetus to the development of international commercial activity and logistics management systems taking full advantage of cross-border networking. The solution lies at the intersection of information technologies, technical means of machine-to-machine (M2M) interaction, mobile high-speed networks, geolocation, cloud services, and a number of international standards. The current trend towards creating digital logistics platforms has set a number of serious challenges for developers. The most important requirement is the condition of sustainability of the obtained solutions with respect to disturbances in the conditions of logistics activities caused not only by market uncertainty but also by a whole set of unfavorable factors accompanying the transportation process. Within the framework of the presented research, the problem of obtaining the conditions for the stability of solutions obtained on the basis of mathematical models is set. At the same time, the processes of transferring not only discrete but also continuous material flows through complex structured networks are taken into account. This study contains the results of the analysis of the stability of solutions of differential systems of various types that simulate the transfer processes in network media. Initial boundary value problems for evolutionary equations and differential-difference systems are relevant in logistics, both for the discrete transportation of a wide range of goods and for the quasi-continuous transportation of, for example, liquid hydrocarbons. The criterion for the work of a logistics operator is the integral functional. For the mathematical description of the transport process of continuous and discrete media, a wide class of integrable functions are used, which adequately describe the transport of media with a complex internal rheological structure.
Highlights
IntroductionSustainability 2021, 13, 9289 changing on a network or a network-like domain (the existence and uniqueness of the solution, the correctness of the stated initial-boundary value problems)
It is a system of parabolic differential equations with distributed parameters a( x ) and b( x ), which characterize the quantitative indicators of the flow state y( x, t) along the edges γ of the graph Γ as a portrait of the logistics network f ( x, t) ∈ L2,1 (Γ T )
Digital logistics is based on some platform-based business models, so the issues of the implementation of digital business models for sustainable development could be a topic for future research
Summary
Sustainability 2021, 13, 9289 changing on a network or a network-like domain (the existence and uniqueness of the solution, the correctness of the stated initial-boundary value problems). The latter led to the emergence of further research by the authors that in 2020 ended with scientific results in the direction of studying the properties of solutions (stability, stabilization, and controllability of system solutions) and the practical use of the obtained results, the logical conclusions of which were the results of this work. The authors note that the results obtained are new—the authors are not aware of similar publications in the studied direction
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