淡江大學機構典藏: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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