| 具有趋化性的非线性系统的解的爆破性态分析 |
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| 引用本文： | 孙贵玲,初元红. 具有趋化性的非线性系统的解的爆破性态分析[J]. 数学的实践与认识, 2013, 43(1) |
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| 作者姓名： | 孙贵玲 初元红 |
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| 作者单位： | 黄河科技学院 信息工程学院,河南郑州,450063 |
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| 摘 要： | 讨论了一个非线性的抛物-椭圆系统,而该系统来源于生物数学中的一个趋化性模型.主要在Sobolev空间的框架下讨论了系统解的爆破性质,得出结论在二维空间中该系统存在一个门槛值,而该值决定了解全局存在或者是发生爆破.最后利用利亚普诺夫函数、下解爆破等方法给出了定理的证明并得出结论.
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| 关 键 词： | 非线性趋化性系统 Keller-Segel模型 利亚普诺夫函数 解的爆破 |
Norm Behavior Of Solutions to a Parabolic-Elliptic System Modeling Chemotaxis in R2 |
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| SUN Gui-ling , CHU Yuan-hong. Norm Behavior Of Solutions to a Parabolic-Elliptic System Modeling Chemotaxis in R2[J]. Mathematics in Practice and Theory, 2013, 43(1) |
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| Authors: | SUN Gui-ling CHU Yuan-hong |
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| Abstract: | We studied a nonlinear parabolic-elliptic system defined on a domain of R2 which comes from a chemotactic system in Biology.We proved the blow up solution of solutions to this problem in Sobolev spaces framework.Next we have the conclusion that there is a critical number which determines the occurrence of blow-up case.Finally,we gave the proof of the theorem with the help of Lyapunov function. |
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| Keywords: | nonlinear chemotaxis system Keller-Segel model Lyapunov function blow up of lower solutions |
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