Stability of weak solutions of parabolic systems with distributed parameters on the graph

Zhabko, Aleksei P.; Shindyapin, Andrey I.; Provotorov, Vyacheslav V.

doi:10.21638/11702/spbu10.2019.404

Cited by 9 publications

(14 citation statements)

References 13 publications

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“…The distribution of the volume of goods over a segment of the commercial network of length L is described by the function Q [48][49][50] obeys the mass transfer equation [51]:…”

Section: Resultsmentioning

confidence: 99%

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Algorithmic Foundations of Economic and Mathematical Modeling of Network Logistics Processes

Barykin

Kapustina

Сергеев

et al. 2020

Journal of Open Innovation: Technology, Market, and Complexity

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Nowadays, digitizing the data stream is enabling the evolution of logistics processes. The data-driven network logistics processes are evaluated by leading economic indicators. The purpose of this study is to further develop the algorithmic foundations of economic and mathematical modeling of logistics networks based on advanced technologies that the digitalization process provides. Methods of mathematical modeling of flows of various resources in logistic networks, the structure of which is presented in the form of a graph, are used in the work. The economic benefit lies in the implementation of the planning concept based on leading indicators. As a result, using a set of formalisms, a mathematical model has been developed, which will make it possible to search for optimal solutions based on the criterion of economic efficiency. The results obtained will find application not only in transport problems. Network logistics includes the transportation of liquid and gaseous materials through pipelines, energy through electrical networks. A universal mathematical model will allow the results to be applied in many industries and economic activities when it is required to make economically sound decisions based on a stream of digital data coming in real time.

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“…The distribution of the volume of goods over a segment of the commercial network of length L is described by the function Q [48][49][50] obeys the mass transfer equation [51]:…”

Section: Resultsmentioning

confidence: 99%

“…The set of linear differential equations given above on edges (1) and the boundary conditions (3) or (4) in boundary nodes which are supplemented with agreement conditions in internal nodes (2) as a whole allow the boundary value problem to be formulated on the graph. In this case h, β are the parameters [50] defined in the process.…”

Section: Main Formalismsmentioning

confidence: 99%

Algorithmic Foundations of Economic and Mathematical Modeling of Network Logistics Processes

Barykin

Kapustina

Сергеев

et al. 2020

Journal of Open Innovation: Technology, Market, and Complexity

View full text Add to dashboard Cite

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“…Let as take in the ratio (9) η(x) = 2τu(k) and granting (10), as well as the lower boundary a * for a(x) (see (2)) get inequality…”

Section: A Weak Solution Of the Initial Boundary Value Problem (1) (mentioning

confidence: 99%

“…Example. We consider the example reduced in the work [10]. Let Γ is a graph-star with edges γ , = 1, 2, 3, and a interior node ξ (to simplify the formulas, let's assume that the edges γ , = 1, 2, are parameterized by a segment [0, π/2], γ 3 is parameterized by a segment [π/2, π]).…”

Section: A Weak Solution Of the Initial Boundary Value Problem (1) (mentioning

confidence: 99%

“…Notations, concepts and basic statements. In the represented work uses concepts and notations accepted in the works [6][7][8][9][10]: Γ is bounded oriented geometric graph with edges γ parameterized segment [0, 1]; ∂Γ and J(Γ) are many boundary ζ and interior ξ nodes of the graph, respectively; Γ 0 is join all the edges of the graph Γ that do not contain endpoints;…”

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confidence: 99%

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Countable stability of a weak solution of a parabolic differential-difference system with distributed parameters on the graph

Provotorov¹,

Сергеев²,

Hoang³

2020

Vestnik SPbSU. Applied Mathematics. Computer Science. Control P

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The article proposes an analog of E. Rothe’s method (semi-discretization with respect to the time variable) for construction convergent different schemes when analyzing the countable stability of a weak solution of an initial boundary value problem of the parabolic type with distributed parameters on a graph in the class of summable functions. The proposed method leads to the study of the input initial boundary value problem to analyze the boundary value problem in a weak setting for elliptical type equations with distributed parameters on the graph. By virtue of the specifics of this method, the stability of a weak solution is understood in terms of the spectral criterion of stability (Neumann’s countable stability), which establishes the stability of the solution with respect to each harmonic of the generalized Fourier series of a weak solution or a segment of this series. Thus, there is another possibility indicated, in addition to the Faedo—Galerkin method, for constructing approaches to the desired solution of the initial boundary value problem, to analyze its stability and the way to prove the theorem of the existence of a weak solution to the input problem. The approach is applied to finding sufficient conditions for the countable stability of weak solutions to other initial boundary value problems with more general boundary conditions — in which elliptical equations are considered with the boundary conditions of the second or third type. Further analysis is possible to find the conditions under which Lyapunov stability is established. The approach can be used to analyze the optimal control problems, as well as the problems of stabilization and stability of differential systems with delay. Presented method of finite difference opens new ways for approximating the states of a parabolic system, analyzing their stability in the numerical implementation and algorithmization of optimal control problems.

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Unleashing the mechanism between small and medium enterprises, and green financing in China: a pathway toward environmental sustainability and green economic recovery

Hou

Zhen

2022

Environ Sci Pollut Res

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In this research, we analyzed green finance, small and medium-sized businesses, and financial literacy in China to boost the green economy. Green finance and financial literacy were examined holistically using a rigorous empirical approach and data envelopment analysis to provide the way to advance green economic recovery in this research. According to empirical evidence, green financing impacts SMEs at 0.31, 0.41, and 2.02 on green economic recovery. China’s green finance and small businesses contribute significantly to the country’s overall green economic revival. A more accurate forecast of green economic recovery was made possible by including other variables such as population expansion, development, and small business development. The analysis used the data envelopment analysis, and the results were solid. Additional hypothetical time-dependent instances demonstrated China’s predicted green financing and small business’s nexus for 2000 to 2020. The proportion of SMEs is decreasing, and as a result, green financing and financial literacy have increased by an average of 12.5% during this time. China’s green financing would fall dramatically if the country’s industrial structure is reduced. According to our findings, financial literacy is positively correlated with green economic recovery, while illiteracy is negatively correlated with growth. Finally, the report provides some ideas for China’s future green economic recovery.

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Stability of weak solutions of parabolic systems with distributed parameters on the graph

Cited by 9 publications

References 13 publications

Algorithmic Foundations of Economic and Mathematical Modeling of Network Logistics Processes

Algorithmic Foundations of Economic and Mathematical Modeling of Network Logistics Processes

Countable stability of a weak solution of a parabolic differential-difference system with distributed parameters on the graph

Unleashing the mechanism between small and medium enterprises, and green financing in China: a pathway toward environmental sustainability and green economic recovery

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