一类具有外部扩散及非线性边界流问题解的爆破  

A Class of Blow-Up Solution with External Diffusion and Nonlinear Boundary Flow Problems

作　　者：李颖韬 潘志刚[1] 

机构地区：[1]西南交通大学数学学院,四川成都 [2]四川大学数学学院,四川成都

出　　处：《应用数学进展》2017年第8期975-984,共10页Advances in Applied Mathematics

基　　金：中央高校理科创新基金项目(No.A0920502051619-113)。

摘　　要：本文研究了一类具有外部扩散及非线性边界流问题,利用构造辅助函数,结合极值原理,利用经典的微分不等式,分别得到了其在Neumman边界和Dirichlet边界下爆破解存在的充分条件,爆破时刻的上界估计,最后给出了定理在两个非线性问题中的具体应用。In this paper, we study a class of problems with external diffusion and nonlinear boundary flow. By using the construction auxiliary function and the maximum principle, the sufficient conditions for the existence of the blow-up solution under the Neumman boundary and the Dirichlet boundary are obtained respectively by using the classical differential inequality. The upper bound of the “blow-up time” is estimated, and finally the concrete application of the theorem in two nonlinear problems is given.

关 键 词：外部扩散 非线性边界 爆破解 爆破时刻 

分 类 号：O1[理学—数学]