一类非线性反应扩散方程爆破时间的下界估计  

Lower Bound Estimates of Blow-up Time for a Class of Nonlinear Reaction-diffusion Equations

作　　者：陈雪姣 李远飞 郭战伟 CHEN Xue-jiao;LI Yuan-fei;GUO Zhan-wei(School of Data Science,Guangzhou Huashang College,Guangzhou 511300,China;Guangdong Communication Polytechnic,Guangzhou 511407,China)

机构地区：[1]广州华商学院数据科学学院,广东广州511300 [2]广东交通职业技术学院基础部,广东广州511407

出　　处：《数学的实践与认识》2021年第22期188-198,共11页Mathematics in Practice and Theory

基　　金：广东省普通高校重点项目(自然科学)(2019KZDXM042);广州华商学院科研团队项目(2021HSKT01)。

摘　　要：研究了三维有界区域上非线性反应扩散方程解在有限时间的爆破问题.假设解在区域的边界上满足非线性条件,当爆破发生时,通过构造辅助函数,利用能量估计的方法和微分不等式技术,得到了爆破时间的下界.在某种特殊的限定条件下,证明了全局解的存在性.The finite time blow-up problem of the solution of nonlinear reaction-diffusion equation in three dimensional bounded domain is studied.Assuming that the solution satisfies the nonlinear conditions at the boundary of the region,the lower bound of the blow-up time are obtained by constructing the auxiliary function and using the energy estimation method and the differential inequality technique when the blow-up occurs.The existence of global solutions is proved under some special limiting conditions.

关 键 词：反应扩散方程 微分不等式技术 下界 全局存在性 

分 类 号：O175[理学—数学]