一类具有空变系数和吸收项的非局部多孔介质系统解的爆破研究  

Blow-up investigation of solutions to a class of nonlocal porous medium systems with space-dependent coefficients and inner absorption terms

作　　者：欧阳柏平 OUYANG Baiping(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,广州511300

出　　处：《华东师范大学学报（自然科学版）》2022年第6期17-29,共13页Journal of East China Normal University(Natural Science)

基　　金：国家自然科学基金(11371175);广东省普通高校重点项目(2019KZDXM042);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)。

摘　　要：研究了一类具有空变系数和吸收项的非局部多孔介质系统在R^(n)(n≥3)上非线性边界条件下解的爆破问题.通过构造能量表达式,运用微分不等式技巧,得到了该问题存在全局解的充分条件.然后应用索伯列夫不等式等技巧实现了爆破发生时解的爆破时间上界和下界的估计.In this paper,we explore the blow-up of solutions to a class of nonlocal porous medium systems with space-dependent coefficients and inner absorption terms under nonlinear boundary conditions in R^(n)(n≥3)sufficient conditions for the global existence of solutions to the problem.Then,upper bound and lower bound estimates of the blow-up time are derived by means of the Sobolev inequalities and other differential methods when blow-up occurs.

关 键 词：爆破 多孔介质系统 空变系数 吸收项 

分 类 号：O175.29[理学—数学]