具有时变系数的非局部混合抛物系统解的爆破  

Blow-up of solutions to a nonlocal mixed parabolic system with time-dependent coefficients

作　　者：欧阳柏平 肖胜中[2] Ouyang Baiping;Xiao Shengzhong(College of Data Science,Guangzhou Huashang College,Guangzhou 511300,China;Scientific Research Department,Guangdong AIB Polytechnic College,Guangzhou 510507,China)

机构地区：[1]广州华商学院数据科学学院,广州511300 [2]广东农工商职业技术学院科研处,广州510507

出　　处：《河南师范大学学报（自然科学版）》2022年第1期82-90,共9页Journal of Henan Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11371175);广东省普通高校创新团队项目(2020WCXTD008);广州华商学院校内项目(2020HSDS01,2021HSKT01).

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局部混合抛物系统解的爆破问题.运用微分不等式技巧,得到了高维空间上非线性边界条件下具有时变系数和吸收项的非局部混合抛物系统全局解的条件.同时,通过构造能量表达式,应用Sobolev不等式等技巧,推出了爆破发生时解的爆破时间下界的估计.Blow-up of solutions to a nonlocal mixed parabolic system with time-dependent coefficients and inner absorption terms under nonlinear boundary conditions is studied.By using a differential technique,the sufficient conditions for the global existence for a nonlocal mixed parabolic system with time-dependent coefficients and inner absorption terms under nonlinear boundary conditions in high spaces are obtained.Furthermore,the lower bound estimate of blow-up time is derived by formulating energy expressions and using Sobolev inequalities and other differential methods.

关 键 词：爆破 抛物系统 全局存在性 时变系数 吸收项 

分 类 号：O175.2[理学—数学]