华东师范大学学报（自然科学版） >

2022 , Vol. 2022 >Issue 6: 30 - 37

DOI: https://doi.org/10.3969/j.issn.1000-5641.2022.06.004

数学

具有非线性梯度项的抛物系统的爆破现象

  • 李远飞
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  • 广州华商学院 数据科学学院, 广州　511300
李远飞, 男, 博士, 特聘教授, 研究方向为偏微分方程. E-mail: liyuanfei@gdhsc.edu.cn

收稿日期: 2021-02-01

  网络出版日期: 2022-11-22

基金资助

广东省普通高校重点项目(2019KZDXM042)

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Blow-up phenomenon of a parabolic system with a nonlinear gradient term

  • Yuanfei LI
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  • School of Data Science, Guangzhou Huashang College, Guangzhou　511300, China

Received date: 2021-02-01

  Online published: 2022-11-22

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摘要

研究了带非线性梯度项的一类抛物方程的解在有限时间内的爆破问题. 当爆破发生时通过构造辅助函数, 利用能量估计的方法和微分不等式, 如果爆破发生, 得到了解的爆破时间的下界. 对方程中的参数做出一定的限制之后, 证明了全局解的存在性.

关键词： 非线性梯度项; 爆破; 下界; 全局存在性

本文引用格式

李远飞 . 具有非线性梯度项的抛物系统的爆破现象[J]. 华东师范大学学报（自然科学版）, 2022 , 2022(6) : 30 -37 . DOI: 10.3969/j.issn.1000-5641.2022.06.004

Abstract

In this paper, the blow-up problem of a parabolic equation with a nonlinear gradient term in finite time is studied. By constructing an auxiliary function, using the method of energy estimation and the differential inequality technique, the lower bound of blow-up time is obtained. After limiting the parameters of the equation, the existence of a global solution is proved.

Key words： nonlinear gradient term; blow-up; lower bound; global existence

参考文献

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