TY - JOUR
T1 - WEIGHTED IRRIGATION PLANS*
AU - Bressan, Alberto
AU - Sun, Qing
N1 - Publisher Copyright:
© 2022. All Rights Reserved.
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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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U2 - 10.4310/CMS.2022.v20.n3.a2
DO - 10.4310/CMS.2022.v20.n3.a2
M3 - Article
AN - SCOPUS:85128256755
SN - 1539-6746
VL - 20
SP - 611
EP - 651
JO - Communications in Mathematical Sciences
JF - Communications in Mathematical Sciences
IS - 3
ER -