带非局部边界条件的反应扩散方程组的爆破现象  

On Blow-up Phenomena in a Reaction-Diffusion Equation Systems with Nonlocal Boundary Conditions

作　　者：李旭敏 崔泽建[1] LI Xumin;CUI Zejian(College of Mathematics and Information, West China Normal University, Nanchong Sichuan 637002, China;Chengdu Kehua Middle Road Primary School, Chengdu 610042, China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637002 [2]成都市科华中路小学,成都610042

出　　处：《西南师范大学学报（自然科学版）》2021年第9期19-26,共8页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11301419);西华师范大学英才科研项目(17YC382).

摘　　要：研究了一类带非局部边界条件的非线性反应扩散方程组解的爆破问题.通过构造恰当的辅助函数,结合改进的微分不等式技巧,建立了解在有限时间爆破的充分条件,得到了爆破时间t^(*)的上界估计;若爆破发生,相应可得t^(*)的下界估计.In this paper,the blow-up of solutions has been investigated to a class of nonlinear reaction-diffusion systems with non-local boundary conditions.By constructing appropriate auxiliary functions and improved differential inequality techniques,sufficient conditions have been established to blow up at some finite time,and then an upper bound of the blow-up time t^(*) has been obtained;moreover,if the blow-up occurred,the lower bound estimation of the blow-up time t^(*) will be got.

关 键 词：反应扩散方程 非局部边界条件 爆破 上下界 

分 类 号：O175.29[理学—数学]