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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

沈旭辉. 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 [J]. 应用数学和力学,2022,43(4):469-476 doi: 10.21656/1000-0887.420155
引用本文: 沈旭辉. 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 [J]. 应用数学和力学,2022,43(4):469-476 doi: 10.21656/1000-0887.420155
SHEN Xuhui. Lower Bounds for Blow-Up Time of Reaction-Diffusion Equations With Gradient Terms and Nonlocal Terms[J]. Applied Mathematics and Mechanics, 2022, 43(4): 469-476. doi: 10.21656/1000-0887.420155
Citation: SHEN Xuhui. Lower Bounds for Blow-Up Time of Reaction-Diffusion Equations With Gradient Terms and Nonlocal Terms[J]. Applied Mathematics and Mechanics, 2022, 43(4): 469-476. 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
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

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

  • 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。

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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

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