一类非线性反应扩散方程爆破解和全局解的存在性  

Blow-Up Solutions and the Existence of Global Solutions for A Class of Nonlinear Reaction-Diffusion Equations

作　　者：侯春娟 李远飞 Hou Chunjuan;Li Yuanfei(School of Data Science,Guangzhou Huashang College,Guangzhou 511300,China)

机构地区：[1]广州华商学院数据科学学院,广东广州511300

出　　处：《海南大学学报（自然科学版）》2022年第1期7-16,共10页Natural Science Journal of Hainan University

基　　金：广东省普通高校青年创新人才项目(自然科学)(2017KQNCX265);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内的爆破问题,并模拟了某些燃烧过程.设解在区域的边界上满足非线性条件,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,证明了解在有限时间内的爆破性结果,得到了爆破时间的上界.在某种特殊的限定条件下,证明了全局解的存在性.In the report,the blow-up problem of the solution of nonlinear reaction diffusion equation in finite time was studied,in which the model simulates some combustion processes.If the solutions satisfy the nonlinear conditions at the boundary of the region,the auxiliary functions are constructed,and the energy estimation method and the differential inequality technique are used to prove the blasting result in a finite time,and the upper bound of the blasting time is obtained.Under some special limiting conditions,the existence of global solutions was proved.

关 键 词：反应扩散方程 微分不等式技术 上界 全局存在性 

分 类 号：O175.29[理学—数学]