一类带有变指数非局部项的反应扩散方程解的爆破行为

田娅; 秦瑶; 向晶

doi:10.21656/1000-0887.420180

一类带有变指数非局部项的反应扩散方程解的爆破行为

doi: 10.21656/1000-0887.420180

重庆邮电大学理学院，重庆 400065

详细信息

作者简介:
田娅（1980—），女，副教授，博士，硕士生导师（通讯作者. E-mail：tianya@cqupt.edu.cn）

秦瑶（1995—），女，硕士生（E-mail：s190603007@stu.cqupt.edu.cn）

向晶（1998—），女，硕士生（E-mail：s200601013@stu.cqupt.edu.cn）

中图分类号: O357.41
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- 文章访问数: 508
- HTML全文浏览量: 185
- PDF下载量: 70
- 被引次数: 0
出版历程
- 收稿日期: 2021-07-01
- 录用日期: 2021-09-29
- 修回日期: 2021-09-09
- 网络出版日期: 2022-09-24
- 刊出日期: 2022-10-31

Blow-Up Behaviors of Solutions to Reaction-Diffusion Equations With Nonlocal Sources and Variable Exponents

School of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, P.R.China

摘要

摘要:
该文考虑了一类带有变指数非局部项的反应扩散方程的爆破问题。首先，由不动点原理，证明了问题解的局部存在性和唯一性。其次，利用上下解方法，给出在齐次Dirichlet边界条件下，问题的解在有限时间发生爆破的充分条件，即变指数大于零且初始值足够大，并对爆破时间的上下界进行了估计。
- 非局部项 /
- 变指数 /
- 有限时间爆破 /
- 爆破时间上下界
Abstract:
The blow-up problems of the solutions are considered for reaction-diffusion equations with nonlocal sources and variable exponents. Firstly, the local existence and uniqueness of solutions to the problem were proved under the fixed-point theorem. Secondly, by means of the super- and sub-solution method, some sufficient conditions for the occurrence of finite-time blow-up were determined under the homogeneous Dirichlet boundary conditions, i.e., the variable exponent is positive and the initial value is large enough. Moreover, the estimates of upper and lower bounds of the blow-up time were given.
- nonlocal source /
- variable exponent /
- blow-up in finite time /
- upper and lower bounds of the blow-up time

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参考文献(16)

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文章访问数: 508
HTML全文浏览量: 185
PDF下载量: 70
被引次数: 0

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一类带有变指数非局部项的反应扩散方程解的爆破行为

doi: 10.21656/1000-0887.420180

作者简介:
田娅（1980—），女，副教授，博士，硕士生导师（通讯作者. E-mail：tianya@cqupt.edu.cn）

秦瑶（1995—），女，硕士生（E-mail：s190603007@stu.cqupt.edu.cn）

向晶（1998—），女，硕士生（E-mail：s200601013@stu.cqupt.edu.cn）

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Blow-Up Behaviors of Solutions to Reaction-Diffusion Equations With Nonlocal Sources and Variable Exponents

计量

目录

留言板

一类带有变指数非局部项的反应扩散方程解的爆破行为

doi: 10.21656/1000-0887.420180

作者简介: 田娅（1980—），女，副教授，博士，硕士生导师（通讯作者. E-mail：tianya@cqupt.edu.cn） 秦瑶（1995—），女，硕士生（E-mail：s190603007@stu.cqupt.edu.cn） 向晶（1998—），女，硕士生（E-mail：s200601013@stu.cqupt.edu.cn）

计量

出版历程

Blow-Up Behaviors of Solutions to Reaction-Diffusion Equations With Nonlocal Sources and Variable Exponents

计量

出版历程

目录

作者简介:
田娅（1980—），女，副教授，博士，硕士生导师（通讯作者. E-mail：tianya@cqupt.edu.cn）

秦瑶（1995—），女，硕士生（E-mail：s190603007@stu.cqupt.edu.cn）

向晶（1998—），女，硕士生（E-mail：s200601013@stu.cqupt.edu.cn）