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.
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.
出处
《数学的实践与认识》
CSCD
北大核心
2013年第1期255-260,共6页
Mathematics in Practice and Theory
基金
河南省教育厅基金(2011C110005)
