一类带对数非线性项的抛物方程解的存在性和爆破

数学物理学报 ›› 2021, Vol. 41 ›› Issue (6): 1816-1829.

一类带对数非线性项的抛物方程解的存在性和爆破

杜玉阁(),田书英*()

^{武汉理工大学理学院武汉 430070}

收稿日期:2020-07-08 出版日期:2021-12-26 发布日期:2021-12-02
通讯作者: 田书英 E-mail:DuYuge@whut.edu.cn;sytian@whut.edu.cn
作者简介:杜玉阁, E-mail:DuYuge@whut.edu.cn
基金资助:
国家自然科学基金(11601402);中央高校基本科研业务费专项资金(2020IA003)

Existence and Blow-Up of a Parabolic Equation with Logarithmic Nonlinearity

Yuge Du(),Shuying Tian*()

^{School of Science, Wuhan University of Technology, Wuhan 430070}

Received:2020-07-08 Online:2021-12-26 Published:2021-12-02
Contact: Shuying Tian E-mail:DuYuge@whut.edu.cn;sytian@whut.edu.cn
Supported by:
the NSFC(11601402);the Fundamental Research Funds for the Central Universities(2020IA003)

摘要/Abstract

摘要：

该文研究具有对数非线性项和粘性项的非线性抛物方程的初边值问题.在一些适当的条件下，得到弱解的全局存在性.关于爆破性方面，得到该方程的解在任何有限时刻不爆破.这与具有多项式非线性项和粘性项的抛物方程有所不同，在那种情况下，方程的解在有限时刻爆破.

关键词: 对数非线性, 粘弹性项, 存在性, 爆破性

Abstract:

In this paper, we consider the initial boundary value problem of a viscoelastic equation with logarithmic nonlinearity. Under some suitable conditions, we obtain the existence of global weak solutions. Otherwise, we get that the solution does not blow up in any finite time. This is different from the situation of the viscoelastic equation with a polynomial nonlinearity, in which case the solution blows up in finite time.

Key words: Logarithmic nonlinearity, Viscoelastic term, Global existence, Blow-up

中图分类号:

O175

杜玉阁,田书英. 一类带对数非线性项的抛物方程解的存在性和爆破[J]. 数学物理学报, 2021, 41(6): 1816-1829.

Yuge Du,Shuying Tian. Existence and Blow-Up of a Parabolic Equation with Logarithmic Nonlinearity[J]. Acta mathematica scientia,Series A, 2021, 41(6): 1816-1829.

参考文献 18

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