一类非线性反应扩散方程在高维空间的爆破解  

Blow-up Solutions for a Class of Reaction-diffusion Equations in High Dimensional Space

作　　者：胡红娟 杜健 鞠桂玲 曹贻鹏 HU Hong-juan;DU Jian;JU Gui-ling;CAO Yi-peng(Basic Department,Army Armoured Academy,Beijing 100072,China)

机构地区：[1]陆军装甲兵学院基础部,北京100072

出　　处：《数学的实践与认识》2022年第2期188-196,共9页Mathematics in Practice and Theory

基　　金：学院自主创新项目(2019CJ111)。

摘　　要：主要讨论了一类具有Dirichlet边界条件的非线性反应扩散方程在高维空间的爆破解.通过构造恰当的辅助函数和利用一阶微分不等式技术,给出了在高维空间下爆破解存在的充分条件以及爆破时刻的上下界.In this paper we investigate the blow-up solutions for a class of nonlinear reaction-diffusion equation with Dirichlet boundary conditions in high dimensional space.By constructing auxiliary functions and using the first-order differential inequality technique,we give the sufficient conditions for the existence of the blow-up.In addition,the lower and upper bounds for the blow-up time when blow-up occurs are also obtained in high dimensional space.

关 键 词：反应扩散方程 高维空间 爆破解 上下界 

分 类 号：O175[理学—数学]