On the short-time behaviour of the free boundary of a porous medium equation
type: Item
instance of: scholarly article
title: On the short-time behaviour of the free boundary of a porous medium equation
zbMATH Open document ID: 0874.35091
DOI: 10.1215/S0012-7094-97-08706-8
author: Carmen Cortázar
author: Manuel Elgueta
author: Manuel del Pino
published in: Duke Mathematical Journal
publication date: 1997-11-10T00:00:00Z
review text: Let \(\Omega\) be a bounded open set in \(\mathbb{R}^N\), \(N\geq 2\), with a smooth boundary \(\Sigma\) and \(m>1\). Consider the problem \[ u_t= \Delta u^m \text{ in } \Omega \times (0,+\infty), \quad u(x,t)=1 \text{ in } \Sigma\times (0,+\infty), \quad u(x,0)=0 \text{ in } \Omega. \] For every \(x_0\) in \(\Omega\) there exists \(T(x_0)\) such that \(u(x_0,t)=0\) for \(0<t< T(x_0)\) and \(u(x_0,t)>0\) for \(t>T(x_0)\). The authors give a precise estimate of \(T(x_0)\) in terms of the geometric properties of \(\Omega\).
reviewed by: Marco Biroli
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35R35
zbMATH DE Number: 1011426
zbMATH Keywords: porous medium equation
zbMATH Keywords: behavior of the free boundary
MaRDI profile type: Publication
cites work: The focusing problem for the radially symmetric porous medium equation
cites work: Self-similarity in the post-focussing regime in porous medium flows
cites work: Q3311022
cites work: The Initial Trace of a Solution of the Porous Medium Equation
cites work: Q3882115
cites work: Q3786839
cites work: How Long Does it Take for a Gas to Fill a Porous Container?
description: scientific article; zbMATH DE number 1011426