| 通过移动媒质避免爆破 |
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| 作者姓名： | YAO Li LIU Yun-xian YANG Peng-fei |
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| 作者单位： | Department of Applied Mathematics，Information Engineering University，Zhengzhou 450002，China; College of Mathematics，Shandong University，Jinan 250100，China |
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| 基金项目： | Supported by the Innovation Project for University Prominent Research Talents of Henan (2003KJCX008) |
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| 摘 要： | This paper deals with two parabolic initial-boundary value problems in multidimensional domain. The first problem describes the situation where the spherical medium is static and the nonlinear reaction takes place only at a single point. We show that under some conditions, the solution blows up in finite time and the blow-up set is the whole spherical medium. When the spherical medium is allowed to move in a special space, we investigate another parabolic initial-boundary value problem. It is proved that the blow-up can be avoided if the acceleration of the motion satisfies certain conditions.
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| 关 键 词： | 抛物型偏微分方程 初边值问题 移动介质 非线性反应 |
Avoidance of Blow-up by Moving Medium |
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| YAO Li,LIU Yun-xian,YANG Peng-fei.Avoidance of Blow-up by Moving Medium[J].Chinese Quarterly Journal of Mathematics,2005,20(2):167-177. |
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| Authors: | YAOLi LIUYun-xian YANGPeng-fei |
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| Institution: | [1]DepartmentofAppliedMathematics,InformationEngineeringUniversity,Zhengzhou450002,China [2]CollegeofMathematics,ShandongUniversity,Jinan250100,China |
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| Abstract: | This paper deals with two parabolic inltial-boundary value problems in multidimensional domain. The first problem describes the situation where the spherical medium is static and the nonlinear reaction takes place only at a single point. We show that under some conditions, the solution blows up in finite time and the blow-up set is the whole spherical medium. When the spherical medium is allowed to move in a special space, we investigate another parabolic initial-boundary value problem. It is proved that the blow-up can be avoided if the acceleration of the motion satisfies certain conditions. |
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| Keywords: | moving medium blow-up parabolic problem |
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