A Fujita type result for a degenerate Neumann problem in domains with noncompact boundary
type: Item
instance of: scholarly article
title: A Fujita type result for a degenerate Neumann problem in domains with noncompact boundary
zbMATH Open document ID: 0920.35079
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-09-01T00:00:00Z
review text: The authors consider the following Neumann problem \[ \begin{aligned} (w^{\beta})_{t} -\text{ div } (| Dw| ^{m-1}Dw) =w^{\nu}, &\quad \text{in} Q_{T},\\ | Dw| ^{m-1}Dw\cdot \mathbf{n}=0, &\quad \text{on} \partial \Omega\times (0,T),\\ w^{\beta}(x,0)= w_{0}^{\beta}(x), &\quad \text{in} \Omega,\end{aligned} \] where \(\Omega\subset {\mathbb R}^{N}\), \(N\geq 2\), is a unbounded domain with noncompact boundary \(\partial \Omega\), \(Q_{T}=\Omega\times(0,T)\), \(T\leq \infty\), \(0<\beta\leq 1\), \(m>1\), \(\nu>1\), \(w_{0}(x)\geq 0\) with \(w^{\beta}_{0}\in L^{1}_{loc}(\bar \Omega)\) and \(\mathbf{n}\) is the unit outward normal to \(\partial \Omega\). The authors study existence or nonexistence of global in time solutions and also derive estimates of the finite speed of propagation of the support of \(w\). It is shown how these properties depend on the geometry of \(\Omega\).
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35K65
zbMATH DE Number: 1274906
zbMATH Keywords: speed of propagation of the support
zbMATH Keywords: global existence and nonexistence
author: Daniele Andreucci
author: A. F. Tedeev
reviewed by: Dian K. Palagachev
MaRDI profile type: Publication
OpenAlex ID: W2039122417
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DOI: 10.1006/JMAA.1998.6253
description: scientific article; zbMATH DE number 1274906