一类基尔霍夫型非线性抛物方程解的存在和爆破  

Existence and Blow-Up of Solutions for a Class of Nonlinear Parabolic Equation with Kirchhoff-Type

作　　者：黄瑶 石鹏 HUANG Yao;SHI Peng(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》2020年第5期80-85,共6页Journal of Hainan Tropical Ocean University

基　　金：贵州民族大学自然科学基金项目〔GZMU(2019)YB04〕。

摘　　要：利用位势井和变分方法,研究了一类基尔霍夫型非线性抛物方程解的存在性以及有限时间内爆破的初始能量.重点研究了初始能量中的亚临界状态(J(u 0)<d),最后通过两个定理的证明验证了该类方程解的存在性以及和时间的关系,进而用数学的方法解决了现实生活当中的物理问题.By applying potential wells and variational methods,the existence of solutions to a class of Kirchhoff-type nonlinear parabolic equations and the initial energy of finite time blow-up were studied.The present research focused on the subcritical state in the initial energy(J(u 0)<d).Finally,after two theorems were proved to verify the existence of the solution to this type of equation and its relationship with time,physical problems in real life are solved by applying the mathematical methods.

关 键 词：位势井 基尔霍夫方程 解的存在性 爆破 

分 类 号：O175.26[理学—数学]