具有时变系数和吸收项的非线性非局部反应扩散系统解的爆破  

Blow-up of solutions to a nonlinear nonlocal reaction-diffusion system with time-dependent coefficients and inner absorption terms

作　　者：欧阳柏平 OUYANG Baiping(College 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：《浙江大学学报（理学版）》2022年第1期27-35,共9页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金资助项目(11371175);广东省普通高校创新团队项目(2020WCXTD008);广东财经大学华商学院校内项目(2020HSDS01);广州市哲学社会科学发展“十三五”规划课题(2019G2GJ209).

摘　　要：研究了非线性边界条件下具有时变系数和吸收项的非线性非局部反应扩散系统解的全局存在性和爆破问题。采用Sobolev不等式及其他微分不等式方法,构造能量表达式,在一定条件下得到了其所满足的微分不等式,进而推出了解的全局存在性和爆破发生时解的爆破时间下界估计。Global existence and blow-up of solutions to a nonlinear nonlocal reaction-diffusion system with time-dependent coefficients and inner absorption terms under nonlinear boundary conditions are studied.Energy expressions are formulated.By using the technique of Sobolev inequalities and other differential ones,the energy satisfying a differential inequality under certain conditions is deduced.Finally,the global existence and lower bound estimates of blow up time are obtained respectively.

关 键 词：全局存在性 爆破 反应扩散系统 时变系数 吸收项 

分 类 号：O175.2[理学—数学]