一类带非局部源的反应扩散方程解的整体存在与爆破  

On Existence of Global Solutions and Blow-up of a Nonlocal Reaction-Diffusion Equation

作　　者：赵阳洋 崔泽建[1] ZHAO Yang-yang;CUI Ze-jian(College of Mathematics and Information,West China Normal University,Nanchong Sichuan 637002,China)

机构地区：[1]西华师范大学数学与信息学院

出　　处：《西南师范大学学报（自然科学版）》2019年第8期34-38,共5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：研究了一类具有非局部内吸收和带有非线性Neumann边界条件的拟线性反应扩散方程的整体解和爆破解.通过构造出适当的辅助函数,利用改进的微分不等式技巧,首先得到了整体解存在的充分条件,然后研究了解在有限时间的爆破,同时得到了解的爆破时间t^*的上界和下界估计.In this paper, an initial-boundary value problem has been investigated for a quasilinear reaction-diffusion equation with weighted nonlocal inner absorption and nonlinear Neumann boundary condition. We establish, respectively, first, sufficient conditions for the existence of global solutions are obtained, and second, the blow-up in finite time is studied and the upper and lower bounds of the blow-up time t^* are obtained.

关 键 词：反应扩散方程 爆破 非线性Neumann边界条件 非局部内吸收 

分 类 号：O175.29[理学—数学]