三维有界区域上具有非线性边界条件的耦合反应-扩散方程解的存在性  

Existence of solutions for coupled reaction diffusion equations with nonlinearboundary conditions in three dimensional bounded domain

作　　者：陈雪姣 李远飞 CHEN Xuejiao;LI Yuanfei(Institute of Mathematics and Statistics,Guangzhou Huashang College,Guangzhou,Guangdong 511300,China)

机构地区：[1]广州华商学院数学与统计研究所,广东广州511300

出　　处：《贵州师范大学学报（自然科学版）》2023年第4期40-47,共8页Journal of Guizhou Normal University：Natural Sciences

基　　金：广东省普通高校创新团队项目(2020WCXTD008);广州华商学院科研团队项目(2021HSKT01);广州华商学院导师制项目(2021HSDS16)。

摘　　要：研究了三维有界区域上带非线性梯度项的一类抛物模型的解在有限时间的爆破问题。假设解在区域的边界上满足非线性条件,当爆破发生时,通过构造辅助函数,利用能量估计的方法和微分不等式技术,得到了爆破时间的下界。对方程中的参数做出一定的限制之后,证明了解的全局存在性。The finite time blow-up problem of a parabolic model with nonlinear gradient term in a three-dimensional bounded domain is studied.Assuming that the solution satisfies the nonlinear condition at the boundary of the domain,the lower bound of blow-up time is obtained by constructing auxiliary function,using energy estimation method and differential inequality technique when blow-up occurs,the global existence of solutions is proved by limiting the parameters in the equations.

关 键 词：非线性梯度项 爆破 下界 全局存在性 

分 类 号：O175.29[理学—数学]