Problems on the loss of heat: Herd instinct versus individual feelings

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Abstract

<br>We discuss several problems concerning steady-state distribution<br>of heat in domains in $\mathbb{R}^3$ that are complementary to a<br>finite number of balls. The study of these problems was initiated<br>by M.~L.~Glasser in 1977. Then, in 1978, M.~L.~Glasser and<br>S.~G.~Davison presented a numerical evidence that the heat flux<br>from two equal balls in $\mathbb{R}^3$ decreases when the balls<br>move closer to each other.<br>%We discuss some questions on the individual rates of heat loss<br>%by shape-invariant components of a contracting compact set.<br>These authors interpreted this result in terms of<br>%questions were inspired by observations on<br>the behaviorial habits of sleeping armadillos, the closer animals<br>to each other, the less heat they lose. Much later, in 2003,<br>A.~Eremenko proved this monotonicity property rigorously and<br>suggested new questions on the heat fluxes.<br><br>The goal of this paper is to survey recent developments in this<br>area, pro
Original languageEnglish
Pages (from-to)1-50
JournalAlgebra i Analiz (English translation: St. Petersburg Mathematical Journal
StatePublished - Sep 10 2021

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