On the Mesa problem
type: Item
instance of: scholarly article
title: On the Mesa problem
zbMATH Open document ID: 0631.35046
DOI: 10.1016/0022-247X(87)90331-3
author: A. Friedman
author: Klaus Höllig
published in: Journal of Mathematical Analysis and Applications
publication date: 1987-01-01T00:00:00Z
review text: Let \(u_ m(x,t)\) denote the solution of \(u_ t=\Delta u^ m\) in \({\mathbb{R}}^ d\times (0,\infty)\) with \(u(x,0)=f(x)\), a prescribed function which is integrable, bounded, continuously differentiable, and star shaped in \({\mathbb{R}}^ d\). The authors study the asymptotic behavior of \(u_ m\) as \(m\to \infty\), proving weak star convergence of (rescaled) solutions in \(L^{\infty}_{loc}({\mathbb{R}}^ d\times (0,\infty))\) to a function V whose profile is a time-dependent mesa with plateau of height \(t^{-1/m}\) and remaining surface coinciding with the initial surface f.
reviewed by: G.Passty
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 35A35
zbMATH DE Number: 4025973
zbMATH Keywords: mesa problem
zbMATH Keywords: asymptotic behavior
zbMATH Keywords: weak star convergence
zbMATH Keywords: time-dependent mesa
MaRDI profile type: Publication
cites work: Q3678248
description: scientific article; zbMATH DE number 4025973