The global existence and finite time extinction of a quasilinear parabolic equation
type: Item
instance of: scholarly article
title: The global existence and finite time extinction of a quasilinear parabolic equation
zbMATH Open document ID: 0959.35104
author: Mingxin Wang
author: Yuanwei Qi
published in: Advances in Differential Equations
publication date: 2000-08-21T00:00:00Z
review text: This paper is concerned with the existence of various positive self-similar solutions of the fast diffusion equation \(u_t = \text{div} (|\nabla u|^{m-1}\nabla u)\) in \(\mathbb{R}^n\times (0,\infty)\) with \(0 < m < 1\), \(n\geq 2\). It is proven that there exist both global and finite time extinction self-similar solutions under appropriate conditions on \(m\) and \(n\). The authors give a detailed information on asymptotic properties of such solutions as \(|x|\) tends to \(\infty\).
reviewed by: Shigeru Sakaguchi
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35K15
zbMATH DE Number: 1493609
zbMATH Keywords: \(p\)-Laplacian
zbMATH Keywords: positive self-similar solutions
zbMATH Keywords: fast diffusion equation
zbMATH Keywords: finite time extinction
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1493609