一类具有时变系数的更一般化非局部高维混合抛物系统在非线性边界条件下解的爆破研究  

Study on blow-up of solutions for a class of more general nonlocalhigh-dimensional mixed parabolic systems with time-varyingcoefficients under nonlinear boundary conditions

作　　者：欧阳柏平 OUYANG Bai-ping(College of Data Science,Guangzhou Huashang College,Guangdong 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：《云南民族大学学报（自然科学版）》2023年第2期259-270,共12页Journal of Yunnan Minzu University:Natural Sciences Edition

基　　金：广东省普通高校重点项目(自然科学)(2019KZDXM042);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).

摘　　要：考虑了非线性边界条件下一类具有时变系数的更一般化非局部高维混合抛物系统解的爆破问题.通过构造辅助函数,应用Sobolev嵌入不等式和其他微分不等式方法,得到了该问题存在全局解和爆破的条件.进一步推出了爆破发生时解的爆破时间上下界.The blow-up problem for a class of more general non-local high dimensional mixed parabolic systems with time-varying coefficients under nonlinear boundary conditions is considered.By constructing auxiliary function and applying Sobolev embedding inequality and other differential inequality methods,the conditions for the existence of global solution and blow-up of the problem are obtained.Furthermore,the upper and lower bounds of the blow-up time of the solution when the blasting occurs are derived.

关 键 词：爆破 混合抛物系统 时变系数 非线性边界条件 

分 类 号：O175.29[理学—数学]