A singular energy line of potential well on evolutionary p-Laplacian with logarithmic source  

作　　者：Gege LIU Jingxue YIN Yong LUO 刘格格;尹景学;罗永

机构地区：[1]School of Mathematical Sciences,South China Normal University,Guangzhou,510631,China

出　　处：《Acta Mathematica Scientia》2025年第2期363-384,共22页数学物理学报(B辑英文版)

基　　金：supported by the NSFC(12171166).

摘　　要：We consider large-time behaviors of weak solutions to the evolutionary p-Laplacian with logarithmic source of time-dependent coefficient.We find that the weak solutions may neither decay nor blow up,provided that the initial data u(·,t_(0))is on the Nehari manifold N:={v∈W_(0)^(1,p)(Ω):I(v,to)=0,||▽v||P^(P)≠0}.This is quite different from the known results that the weak solutions may blow up as,u(·,to)∈N^(+):={v∈W_(0)^(1,p)(Ω):I(v,t_(0))<0}and weak solutions may decay as u(·,t_(0))∈N^(+):={v∈W_(0)^(1,p)(Ω):I(v,t_(0))>0}.

关 键 词：logarithmic source singular energy line large-time behavior 

分 类 号：O175.2[理学—数学]