高维空间上具有时变系数和吸收项的非线性非局部抛物方程解的全局存在性和爆破  

Global Existence and Blow-up of Solutions to a Nonlinear Nonlocal Parabolic Equation with Time-Dependent Coefficient and Inner Absorption Term in High Spaces

作　　者：欧阳柏平 OUYANG Bai-ping(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：《内蒙古师范大学学报（自然科学版）》2022年第4期346-352,共7页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：广东省普通高校重点科研资助项目(自然科学)(2019KZDXM042);广东省普通高校创新团队资助项目(2020WCXTD008);广州华商学院校内资助项目(2020HSDS01)。

摘　　要：研究高维空间上具有时变系数和吸收项的非线性非局部抛物方程解的全局存在性和爆破问题。通过构造能量表达式,运用Sobolev不等式及其他微分不等式,在一定约束条件下得到该能量方程所满足的微分不等式。进而推出解的全局存在性和爆破发生时解的爆破时间下界的估计。Global existence and blow-up of solutions to a nonlinear nonlocal parabolic equation with timedependent coefficient and inner absorption term in high spaces are investigated in the paper.Through formulating energy expressions,a differential inequality under some constraint conditions satisfying the energy expressions is derived by using the technique of a Sobolev inequality and other differential inequalities.Then,the global existence,as well as lower bound estimates of solution at blow up time is obtained respectively.

关 键 词：全局存在性 爆破 抛物方程 

分 类 号：O175.2[理学—数学]