Blowing up at zero points of potential for an initial boundary value problem

機構典藏 > College of Sciences > Graduate Institute & Department of Mathematics > Journal Article > Item 987654321/58127

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Title:	Blowing up at zero points of potential for an initial boundary value problem
Authors:	Guo, Jong-Shenq;Shimojo, Masahiko
Contributors:	淡江大學數學學系
Keywords:	Blow up;Potential;Semilinear heat equation;Threshold solution
Date:	2011-01
Issue Date:	2011-09-29 15:27:46 (UTC+8)
Publisher:	Springfield: American Institute of Mathematical Sciences
Abstract:	We study nonnegative radially symmetric solutions for a semilinear heat equation in a ball with spatially dependent coeﬃcient which vanishes at the origin. Our aim is to construct a solution that blows up at the origin where there is no reaction. For this, we ﬁrst prove that the blow-up is complete, if the origin is not a blow-up point and if there is no blow-up point on the boundary. Then we prove that a threshold solution exists such that it blows up in ﬁnite time incompletely and there is no blow-up point on the boundary. On the other hand, we prove that any zero of nonnegative potential is not a blow-up point for a more general problem under the assumption that the solution is monotone in time.
Relation:	Communications on Pure and Applied Analysis 10(1), pp.161-177
DOI:	10.3934/cpaa.2011.10.161
Appears in Collections:	[Graduate Institute & Department of Mathematics] Journal Article

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