具有对数非线性项和分数阶p拉普拉斯算子的抛物方程解的爆破性质  

Blow-Up Properties of Solution for a Parabolic Equations Involving the Fractional p-Laplacian with Logarithmic Nonlinearity

作　　者：时蒙蒙 王建[1] Shi Mengmeng;Wang Jian(School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China)

机构地区：[1]中国海洋大学数学科学学院,山东青岛266100

出　　处：《中国海洋大学学报（自然科学版）》2022年第4期138-146,共9页Periodical of Ocean University of China

基　　金：国家自然科学基金项目(11671188)资助。

摘　　要：本文研究带有分数阶p拉普拉斯算子和对数非线性项的一类抛物方程齐次Dirichlet初边值问题解的爆破性质。利用位势阱理论和凹凸性方法,讨论了负初始能量、次临界初始能量和任意正初始能量下解的有限爆破。此外,本文还得到了适当假设条件下爆破时间的上下界。This paper deals with the blow-up properties of solutions for null Dirichlet initial boundary value problem of parabolic equations involving the fractional p-Laplacian with logarithmic nonlinearity.Applying potential well theory and concave conex method,the authors discuss the blow up of solutions in finite time with three initial energy levels negative,critical and arbitrary positive initial energy levels.Morever,the upper and lower bounds of the blasting time under appropriate assumptions are derived.

关 键 词：分数阶 p拉普拉斯算子 对数非线性项 有限爆破 爆破时间 

分 类 号：O175.29[理学—数学]