Spatial critical points of nonnegative solutions of the evolution \(p\)-Laplacian equation: the fast diffusion case
type: Item
instance of: scholarly article
title: Spatial critical points of nonnegative solutions of the evolution \(p\)-Laplacian equation: the fast diffusion case
zbMATH Open document ID: 0940.35117
author: Shigeru Sakaguchi
published in: Differential and Integral Equations
publication date: 2000-05-22T00:00:00Z
review text: From author's abstract: We consider the Cauchy problem for the fast diffusion equation: \[ \partial _tu=\text{div} (|\nabla u|^{p-2}\nabla u) \text{ in } \mathbb{R}^n\times (0,\infty)\quad \text{and} \quad u(x,0)=\phi (x) \text{ in } \mathbb{R}^n \] with \( 1<p<2 \) for nonzero bounded nonnegative initial data \(\phi \) having compact support, and show that the set of positive spatial critical points of the nonnegative solution is contained in the closed convex hull of the support of the initial datum for any time either when \({3\over 2}<p<2\) and \(N\geq 2\) or when \(1<p<2\) and \(N=1,\) and further in the case \(N=1\) it consists of one point after a finite time.
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35B05
zbMATH DE Number: 1450167
zbMATH Keywords: compactly supported bounded nonnegative initial data
reviewed by: Marie Kopáčková
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1450167