Polygonal heat conductors with a stationary hot spot
type: Item
instance of: scholarly article
title: Polygonal heat conductors with a stationary hot spot
zbMATH Open document ID: 1176.35013
author: Rolando Magnanini
author: Shigeru Sakaguchi
published in: Journal d'Analyse Mathématique
publication date: 2008-10-16T00:00:00Z
review text: Let \(\Omega\) be a convex polygon whose incircle touches every side of \(\partial\Omega\). Consider the heat equation under constant (positive) initial datum and zero boundary conditions. The hot spot is the point at which the temperature attains its spatial maximum at each given time. If the hot spot is stationary, the authors derive two necessary geometric conditions on the geometry of \(\Omega\). In special cases these conditions imply symmetries, provided \(\Omega\) is a pentagon or hexagon.
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 35B38
zbMATH DE Number: 5351755
zbMATH Keywords: symmetry
zbMATH Keywords: convex polygon
zbMATH Keywords: constant initial datum
zbMATH Keywords: zero boundary conditions
MaRDI profile type: Publication
full work available at URL: s11854-008-0029-1
OpenAlex ID: W2048780055
cites work: On extensions of the Brunn-Minkowski and Prekopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
cites work: Q4356412
cites work: The spatial critical points not moving along the heat flow
cites work: Matzoh ball soup: Heat conductors with a stationary isothermic surface
cites work: On heat conductors with a stationary hot spot
cites work: Diffusion processes in a small time interval
DOI: 10.1007/S11854-008-0029-1
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description: scientific article; zbMATH DE number 5351755