华东师范大学学报（自然科学版） ›› 2022, Vol. 2022 ›› Issue (6): 17-29.doi: 10.3969/j.issn.1000-5641.2022.06.003

• 数学 • 上一篇    下一篇

一类具有空变系数和吸收项的非局部多孔介质系统解的爆破研究

欧阳柏平()   

  1. 广州华商学院 数据科学学院, 广州　511300
  • 收稿日期:2021-02-01 出版日期:2022-11-25 发布日期:2022-11-22
  • 作者简介:欧阳柏平, 男, 讲师, 研究方向为偏微分方程. E-mail: oytengfei79@gdhsc.edu.cn
  • 基金资助:
    国家自然科学基金(11371175); 广东省普通高校重点项目(2019KZDXM042); 广东省普通高校创新团队项目(2020WCXTD008); 广州华商学院校内项目(2020HSDS01)

Blow-up investigation of solutions to a class of nonlocal porous medium systems with space-dependent coefficients and inner absorption terms

Baiping OUYANG()   

  1. School of Data Science, Guangzhou Huashang College, Guangzhou　511300, China
  • Received:2021-02-01 Online:2022-11-25 Published:2022-11-22

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摘要：

研究了一类具有空变系数和吸收项的非局部多孔介质系统在 ${\mathbb{R}}^{n}\left(n \geqslant 3\right)$ 上非线性边界条件下解的爆破问题. 通过构造能量表达式, 运用微分不等式技巧, 得到了该问题存在全局解的充分条件. 然后应用索伯列夫不等式等技巧实现了爆破发生时解的爆破时间上界和下界的估计.

关键词: 爆破, 多孔介质系统, 空变系数, 吸收项

Abstract:

In this paper, we explore the blow-up of solutions to a class of nonlocal porous medium systems with space-dependent coefficients and inner absorption terms under nonlinear boundary conditions in ${\mathbb{R}}^{n}\left(n \geqslant 3\right)$ . By constructing an energy expression and using the differential inequality technique, we obtain sufficient conditions for the global existence of solutions to the problem. Then, upper bound and lower bound estimates of the blow-up time are derived by means of the Sobolev inequalities and other differential methods when blow-up occurs.

Key words: blow-up, porous medium system, space-dependent coefficient, inner absorption term

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