一类带对数非线性源项的p-Laplace抛物方程解的存在性与爆破  

Global Existence and Blow-up of Solutions for a Class of p-Laplacian Parabolic Equations with Logarithmic Nonlinearity

作　　者：温兰 杨晗[1] WEN Lan;YANG Han(School of Mathematics,Southwest Jiaotong University,Chengdu 611756,China)

机构地区：[1]西南交通大学数学学院,四川成都611756

出　　处：《应用数学》2022年第3期544-552,共9页Mathematica Applicata

基　　金：国家自然科学基金(11701477,11971394)。

摘　　要：本文研究带对数非线性源项的p-Laplace抛物方程的初边值问题.首先利用Galerkin方法证明方程局部解存在性;然后结合势井方法得出初值在稳定集中时方程整体解的存在性;最后再通过构造合适的辅助泛函,证明当初始能量满足适当条件时解在有限时刻的爆破.This paper is concerned with the initial boundary value problem of a class of p-Laplacian parabolic equations with logarithmic nonlinearity.Firstly,existence of local solutions are obtained by applying Galerkin ’s method.Then,combining with potential well method,it is proved that the solutions exist globally when initial value is in a stable set.Lastly,finite time blow-up results are derived as well by constructing auxiliary functional when the initial energy satisfies suitable conditions.

关 键 词：抛物方程 对数非线性源项 整体解 爆破 

分 类 号：O175.26[理学—数学]