Quantitative unique continuation for the heat equations with inverse square potential

Abstract In this paper, we investigate the unique continuation properties for multi-dimensional heat equations with inverse square potential in a bounded convex domain Ω of Rd $\mathbb{R}^{d}$. We establish observation estimates for solutions of equations. Our result shows that the value of the solu...

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Main Authors:	Guojie Zheng, Keqiang Li, Yuanyuan Zhang
Format:	Article
Language:	English
Published:	SpringerOpen 2018-11-01
Series:	Journal of Inequalities and Applications
Subjects:	Heat equations Singular potential Unique continuation Frequency function
Online Access:	http://link.springer.com/article/10.1186/s13660-018-1907-4

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spelling	doaj-26dfa15a7aa84a10a8eecd883c49e0662020-11-25T02:21:20ZengSpringerOpenJournal of Inequalities and Applications1029-242X2018-11-012018111310.1186/s13660-018-1907-4Quantitative unique continuation for the heat equations with inverse square potentialGuojie Zheng0Keqiang Li1Yuanyuan Zhang2College of Mathematics and Information Science, Henan Normal UniversityCollege of Mathematics and Information Science, Henan Normal UniversityXinxiang No. 7 Middle SchoolAbstract In this paper, we investigate the unique continuation properties for multi-dimensional heat equations with inverse square potential in a bounded convex domain Ω of Rd $\mathbb{R}^{d}$. We establish observation estimates for solutions of equations. Our result shows that the value of the solutions can be determined uniquely by their value on an open subset ω of Ω at any given positive time L.http://link.springer.com/article/10.1186/s13660-018-1907-4Heat equationsSingular potentialUnique continuationFrequency function
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Guojie Zheng Keqiang Li Yuanyuan Zhang
spellingShingle	Guojie Zheng Keqiang Li Yuanyuan Zhang Quantitative unique continuation for the heat equations with inverse square potential Journal of Inequalities and Applications Heat equations Singular potential Unique continuation Frequency function
author_facet	Guojie Zheng Keqiang Li Yuanyuan Zhang
author_sort	Guojie Zheng
title	Quantitative unique continuation for the heat equations with inverse square potential
title_short	Quantitative unique continuation for the heat equations with inverse square potential
title_full	Quantitative unique continuation for the heat equations with inverse square potential
title_fullStr	Quantitative unique continuation for the heat equations with inverse square potential
title_full_unstemmed	Quantitative unique continuation for the heat equations with inverse square potential
title_sort	quantitative unique continuation for the heat equations with inverse square potential
publisher	SpringerOpen
series	Journal of Inequalities and Applications
issn	1029-242X
publishDate	2018-11-01
description	Abstract In this paper, we investigate the unique continuation properties for multi-dimensional heat equations with inverse square potential in a bounded convex domain Ω of Rd $\mathbb{R}^{d}$. We establish observation estimates for solutions of equations. Our result shows that the value of the solutions can be determined uniquely by their value on an open subset ω of Ω at any given positive time L.
topic	Heat equations Singular potential Unique continuation Frequency function
url	http://link.springer.com/article/10.1186/s13660-018-1907-4
work_keys_str_mv	AT guojiezheng quantitativeuniquecontinuationfortheheatequationswithinversesquarepotential AT keqiangli quantitativeuniquecontinuationfortheheatequationswithinversesquarepotential AT yuanyuanzhang quantitativeuniquecontinuationfortheheatequationswithinversesquarepotential
_version_	1724866992286990336

Quantitative unique continuation for the heat equations with inverse square potential

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