Remarks on the zero set of a solution of a parabolic equation in space dimension 1
type: Item
instance of: scholarly article
title: Remarks on the zero set of a solution of a parabolic equation in space dimension 1
zbMATH Open document ID: 0919.35012
author: Kinji Watanabe
published in: Journal of the Mathematical Society of Japan
publication date: 1998-08-09T00:00:00Z
review text: Let \(u\) be a nontrivial solution of the parabolic equation \(u_t= u_{xx}+ q(x,t)u\), \((x,t)\in (0,1)\times (0,T)\), satisfying a certain mixed boundary condition. The author shows that for any point \((x_0,t_0)\in (0,1)\times (0,T)\) where \(u(x_0, t_0)= u_x(x_0, t_0)= 0\), there exists a neighbourhood in which the zero set of \(u\) only consists in a finite union of curves.
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35K20
zbMATH DE Number: 1185530
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/04940817
OpenAlex ID: W1968530851
DOI: 10.2969/JMSJ/04940817
description: scientific article; zbMATH DE number 1185530