具有梯度源和非局部源的反应扩散方程解的爆破时刻下界  

Lower Bounds for Blow-Up Time of Reaction-Diffusion Equations With Gradient Terms and Nonlocal Terms

作　　者：沈旭辉 SHEN Xuhui(School of Applied Mathematics,Shanxi University of Finance and Economics,Taiyuan 030006,P.R.China)

机构地区：[1]山西财经大学应用数学学院,太原030006

出　　处：《应用数学和力学》2022年第4期469-476,共8页Applied Mathematics and Mechanics

基　　金：山西省高等学校科技创新项目(2020L0259)。

摘　　要：对于反应扩散方程解的爆破时刻研究,不仅具有理论意义,而且与安全地控制生产,控制种群密度以及环境趋化治理等实际问题密切相关.该文考虑了一类具有梯度源和非局部源的反应扩散方程解的爆破时刻下界.首先,假设区域为高维空间中的具有光滑边界的有界凸区域;其次,通过构造合适的辅助函数,利用一阶微分不等式技术和Sobolev不等式,得出解在有限时刻发生爆破时的爆破时刻下界;最后,通过两个应用实例来解释说明文中所获得的抽象结论.The research on the blow-up time of solutions to the reaction-diffusion equations has much theoretical significance. Moreover, it is closely related to practical problems such as production safety control, population density control and environmental chemotaxis control. The lower bounds for the blow-up time of solutions to a class of reactiondiffusion equations with gradient terms and nonlocal terms, were considered. Firstly, the region was assumed to be a bounded convex one with smooth boundary in the high-dimensional space. Secondly, through the establishment of suitable auxiliary functions, and with the 1st-order differential inequality and the Sobolev inequality, the lower bounds for the blowup time were derived for finite-time blow-up occurences. Finally, 2 application examples illustrate the abstract results obtained with this method.

关 键 词：反应扩散方程 梯度源 非局部源 爆破时刻 

分 类 号：O175.29[理学—数学]