THRESHOLD RESULT FOR SEMILINEAR PARABOLIC EQUATIONS WITH INDEFINITE NON-HOMOGENEOUS TERM  

作　　者：谢君辉 戴求亿 刘芳 

机构地区：[1]Department of Mathematics,Hunan Normal University

出　　处：《Acta Mathematica Scientia》2012年第6期2302-2314,共13页数学物理学报（B辑英文版）

基　　金：supported by Natural Science Foundation of China(10971061);Hunan Provincial Innovation Foundation For Postgraduate(CX2010B209)

摘　　要：In this paper, we study the threshold result for the initial boundary value problem of non-homogeneous semilinear parabolic equations {μt-△μ=g（μ）＋λf（x）,（x,t）∈Ω×（0,T）,μ=0,（x,t）∈ Ω×[0,T）,μ（x,0）=μ0（x）≥0,x∈Ω.By combining a priori estimate of global solution with property of stationary solution set of problem （P）, we prove that the minimal stationary solution Uλ（x） of problem （P） is stable, whereas, any other stationary solution is an initial datum threshold for the existence and nonexistence of global solution to problem （P）.In this paper, we study the threshold result for the initial boundary value problem of non-homogeneous semilinear parabolic equations {μt-△μ=g（μ）＋λf（x）,（x,t）∈Ω×（0,T）,μ=0,（x,t）∈ Ω×[0,T）,μ（x,0）=μ0（x）≥0,x∈Ω.By combining a priori estimate of global solution with property of stationary solution set of problem （P）, we prove that the minimal stationary solution Uλ（x） of problem （P） is stable, whereas, any other stationary solution is an initial datum threshold for the existence and nonexistence of global solution to problem （P）.

关 键 词：parabolic equations initial boundary value problem global solution thresh-old result non-homogenous tern： 

分 类 号：O175.26[理学—数学]