摘要
在二维空间中讨论了一个抛物-椭圆系统,而该系统来源于生物学中的趋化性模型.主要在Sobolev空间的框架下讨论了解的全局存在性与解的爆破性质,得出结论该系统存在一个门槛值,而该值决定了解全局存在或者发生爆破.最后利用利李亚普诺夫函数给出了定理的证明并得出结论.
We studied a parabolic-elliptic system defined on a domain of R2 which comes from a chemotactic system in Biology. We proved the existence in time or blow up solution to this problem in Sobolev spaces framework. Next we proved 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.
出处
《数学的实践与认识》
CSCD
北大核心
2012年第13期222-227,共6页
Mathematics in Practice and Theory
基金
河南省教育厅基金项目(2011C110005)
