具有非线性梯度项的抛物系统的爆破现象

doi:10.3969/j.issn.1000-5641.2022.06.004

华东师范大学学报（自然科学版） ›› 2022, Vol. 2022 ›› Issue (6): 30-37.doi: 10.3969/j.issn.1000-5641.2022.06.004

具有非线性梯度项的抛物系统的爆破现象

李远飞()

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: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
基金资助:
广东省普通高校重点项目(2019KZDXM042)

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

Yuanfei LI()

School of Data Science, Guangzhou Huashang College, Guangzhou　511300, China

Received:2021-02-01 Online:2022-11-25 Published:2022-11-22

摘要/Abstract

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

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

中图分类号:

O175.29

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.

Yuanfei LI. Blow-up phenomenon of a parabolic system with a nonlinear gradient term[J]. Journal of East China Normal University(Natural Science), 2022, 2022(6): 30-37.

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具有非线性梯度项的抛物系统的爆破现象

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

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