Singular solutions of a superlinear parabolic equation with homogeneous Neumann boundary conditions

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• 作者：Khin Phyu Phyu Htoo^a ; Eiji Yanagida^b ; ^{yanagida@math.titech.ac.jp}
• 关键词：primary ; 35K58 ; secondary ; 35K45 ; 35B33
• 刊名：Nonlinear Analysis: Theory, Methods & Applications
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：151
• 期：Complete
• 页码：96-108
• 全文大小：594 K
• 卷排序：151

文摘

This paper discusses the existence of singular solutions of a superlinear parabolic partial differential equation on bounded domains with homogeneous Neumann boundary conditions. It is shown that in some parameter range, there exists a solution with a spatial singularity whose position and strength depend on time. Both interior and boundary singularities are studied.