Blow-Up and Decay Estimate in a Logarithmic p-Laplace Parabolic Equation  

一类对数p-Laplace抛物型方程中的爆破和衰减估计

作　　者：LI Ping LI Feng-jie 李平;李锋杰

机构地区：[1]College of Science,China University of Petroleum,Qingdao 266580,China

出　　处：《Chinese Quarterly Journal of Mathematics》2024年第4期331-354,共24页数学季刊（英文版）

基　　金：Supported by Shandong Provincial Natural Science Foundation of China(Grant No.ZR2021MA003).

摘　　要：This paper deals with an initial-boundary value problem of a fourth-order parabolic equation involving Logarithmic type p-Laplacian,which could be proposed as a model for the epitaxial growth of thin films.By using the variational method and the logarithmic type Sobolev inequality,we give some threshold results for blow-up solutions and global solutions,which could be classified by the initial energy.The asymptotic estimates about blow-up time and decay estimate of weak solutions are obtained.

关 键 词：High order parabolic equation Blow-up time Decay estimate Global existence Logarithmic type p-Laplacian 

分 类 号：O175.4[理学—数学]