Overview
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 1955)
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Table of contents (15 chapters)
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Front Matter
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Back Matter
Keywords
About this book
The transportation problem can be formalized as the problem of finding the optimal way to transport a given measure into another with the same mass. In contrast to the Monge-Kantorovitch problem, recent approaches model the branched structure of such supply networks as minima of an energy functional whose essential feature is to favour wide roads. Such a branched structure is observable in ground transportation networks, in draining and irrigation systems, in electrical power supply systems and in natural counterparts such as blood vessels or the branches of trees.
These lectures provide mathematical proof of several existence, structure and regularity properties empirically observed in transportation networks. The link with previous discrete physical models of irrigation and erosion models in geomorphology and with discrete telecommunication and transportation models is discussed. It will be mathematically proven that the majority fit in the simple model sketched in this volume.
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Authors and Affiliations
Bibliographic Information
Book Title: Optimal Transportation Networks
Book Subtitle: Models and Theory
Authors: Marc Bernot, Vicent Caselles, Jean-Michel Morel
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-540-69315-4
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2009
Softcover ISBN: 978-3-540-69314-7Published: 23 September 2008
eBook ISBN: 978-3-540-69315-4Published: 23 October 2008
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: X, 200
Number of Illustrations: 53 b/w illustrations, 5 illustrations in colour
Topics: Calculus of Variations and Optimal Control; Optimization, Operations Research, Management Science, Engineering Economics, Organization, Logistics, Marketing, Operations Research/Decision Theory, Applications of Mathematics