Doubly Nonlinear Degenerate Parabolic Equations with a Singular Potential for Greiner Vector Fields  

作　　者：HAN Junqiang 

机构地区：[1]School of Mathematics and Statistics,Northwestern Polytechnical University,Xi'an 710129,China

出　　处：《Journal of Partial Differential Equations》2022年第4期307-319,共13页偏微分方程（英文版）

基　　金：support from Nature Science Fund of China(No.11771354).

摘　　要：The purpose of this paper is to investigate the nonexistence of positive so lutions of the following doubly nonlinear degenerate parabolic equations:{∂u=▽k·(u^(m-1)|▽ku|^(p-2)▽ku)+(w)u^(m+p-2),u(w,0)=u0(w)≥0,u(w,t)=0,inΩ×(0,T),inΩ,on∂Ω×(0,T),where Q is a Carnot-Carathéodory metric bal in IR^(2n+1)generated by Greiner vector fields,V∈L_(loc)(Ω),k∈N,m∈R,1<p<2n+2k and m+p-2>0.The better lower bound p*for m+p is found and the nonexistence results are proved for p*≤m+p<3.

关 键 词：Doubly nonlinear degenerate parabolic equations Greiner vector fields positive solutions NONEXISTENCE Hardy inequality 

分 类 号：O175.29[理学—数学]