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

沈旭辉

doi:10.21656/1000-0887.420155

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

doi: 10.21656/1000-0887.420155

沈旭辉

山西财经大学应用数学学院，太原 030006

基金项目: 山西省高等学校科技创新项目(2020L0259)

详细信息

作者简介:
沈旭辉(1990—)，男，讲师，博士(E-mail：xhuishen@sxufe.edu.cn)

中图分类号: O175.29
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- 文章访问数: 741
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- PDF下载量: 70
- 被引次数: 0
出版历程
- 收稿日期: 2021-06-07
- 修回日期: 2021-08-19
- 网络出版日期: 2022-03-14
- 刊出日期: 2022-04-01

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

SHEN Xuhui

School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, P.R.China

摘要

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。
- 反应扩散方程 /
- 梯度源 /
- 非局部源 /
- 爆破时刻
Abstract:
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 reaction-diffusion 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 blow-up time were derived for finite-time blow-up occurences. Finally, 2 application examples illustrate the abstract results obtained with this method.
- reaction-diffusion equation /
- gradient term /
- nonlocal term /
- blow-up time

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参考文献(20)

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