通过收费站的最佳运输方式

IF 2.3 4区数学 Q1 MATHEMATICS, APPLIED

European Journal of Applied Mathematics Pub Date : 2024-09-18 DOI:10.1017/s0956792524000317

Arthur Stephanovitch, Anqi Dong, Tryphon T. Georgiou

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引用次数: 0

摘要

我们要解决的问题是，在二次成本函数的作用下，通过路径上的一个限制条件，对流量进行优化运输。在概念上，该限制条件由收费站表示，限制了通过该限制条件的流量。我们提供了一个精确的公式，此外，它还可以在更高的维度上进行推广。我们通过证明解的存在性和唯一性，详细研究了一维运输的情况。在适当的正则性假设下，我们给出了运输计划的明确构造。我们还讨论了将通量约束推广到更高维度以及理论的可能扩展。

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Optimal transport through a toll station

We address the problem of optimal transport with a quadratic cost functional and a constraint on the flux through a constriction along the path. The constriction, conceptually represented by a toll station, limits the flow rate across. We provide a precise formulation which, in addition, is amenable to generalization in higher dimensions. We work out in detail the case of transport in one dimension by proving existence and uniqueness of solution. Under suitable regularity assumptions, we give an explicit construction of the transport plan. Generalization of flux constraints to higher dimensions and possible extensions of the theory are discussed.

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来源期刊

European Journal of Applied Mathematics 数学-应用数学

CiteScore

4.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Since 2008 EJAM surveys have been expanded to cover Applied and Industrial Mathematics. Coverage of the journal has been strengthened in probabilistic applications, while still focusing on those areas of applied mathematics inspired by real-world applications, and at the same time fostering the development of theoretical methods with a broad range of applicability. Survey papers contain reviews of emerging areas of mathematics, either in core areas or with relevance to users in industry and other disciplines. Research papers may be in any area of applied mathematics, with special emphasis on new mathematical ideas, relevant to modelling and analysis in modern science and technology, and the development of interesting mathematical methods of wide applicability.