一类分数阶拉普拉斯方程解的存在性与爆破性  

Existence and Blow-up of Solutions for a Class of Fractional Laplacian Equations

作　　者：邓启刚 石鹏 曾福庚 DENG Qigang;SHI Peng;ZENG Fugeng(College of Data Science and Information Engineering,Guizhou Minzu University,Guiyang 550025,China)

机构地区：[1]贵州民族大学数据科学与信息工程学院,贵阳550025

出　　处：《海南热带海洋学院学报》2021年第2期58-65,共8页Journal of Hainan Tropical Ocean University

基　　金：贵州省科学技术基金项目(黔科合基础-ZK〔2021〕一般317)。

摘　　要：针对一类分数阶拉普拉斯方程的初边值问题,采用Galerkin近似和位势井理论以及Nehari流形等方法,结合变分原理、函数收敛等理论证明了在低初始能量J(u_(0))<d的情形下分数阶拉普拉斯方程解的存在性与爆破性,并给出了有限时间爆破的充分条件。Aiming at the initial boundary value problem for a class of fractional Laplacian equations,by applying the methods of Galerkin approximation,potential well theory and Nehari manifold,and combining with the variational principle and function convergence theory,the global existence and finite time blow-up of solutions were discussed in the case of low initial energy J(u_(0))<d.Moreover,the sufficient conditions of the finite time blow-up was given.

关 键 词：拉普拉斯算子 弱解 存在性 爆破性 分数阶 

分 类 号：O175.26[理学—数学]