Weighted irrigation plans

We model an irrigation network where lower branches must be thicker in order to support the weight of the higher ones. This leads to a countable family of ODEs, one for each branch, that must be solved by backward induction. Having introduced conditions that guarantee the existence and uniqueness of solutions, our main result establishes the lower semicontinuity of the corresponding cost functional, w.r.t. pointwise convergence of the irrigation plans. In turn, this yields the existence of an optimal irrigation plan, in the presence of these additional weights.

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Metadata

Work Title Weighted irrigation plans
Access
Open Access
Creators
  1. Alberto Bressan
  2. Qing Sun
Keyword
  1. Ramified transport
  2. Irrigation plan
  3. Impulsive differential equations on networks
License In Copyright (Rights Reserved)
Work Type Article
Publisher
  1. Communications in Mathematical Sciences
Publication Date March 21, 2022
Publisher Identifier (DOI)
  1. https://doi.org/10.4310/CMS.2022.v20.n3.a2
Deposited July 19, 2022

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Work History

Version 1
published

  • Created
  • Added ramif-struct_A.pdf
  • Added Creator Alberto Bressan
  • Added Creator Qing Sun
  • Published
  • Updated Work Title, Keyword, Publication Date Show Changes
    Work Title
    • WEIGHTED IRRIGATION PLANS*
    • Weighted irrigation plans
    Keyword
    • Ramified transport, Irrigation plan, Impulsive differential equations on networks
    Publication Date
    • 2022-01-01
    • 2022-03-21
  • Updated