退化抛物型方程弱解的存在性  

On the Existence of Weak Solutions to a Parabolic Equation of Degenerate Type for Semiconductors

作　　者：周文华[1] 

机构地区：[1]淮海工学院理学院,连云港222005

出　　处：《数学学报（中文版）》2010年第3期495-502,共8页Acta Mathematica Sinica：Chinese Series

基　　金：淮海工学院科研课题资助项目(Z2007024)

摘　　要：讨论初值为u_0,v_0∈L_+~4(Ω),w∈W^(1,p)(Ω)(p≥2)时退化抛物型方程弱解的存在性.首先利用截断的方法将原问题正则化,化为u_0,v_0∈L_+~∞(Ω)的退化问题,接着对正则化问题的解做估计(这里的估计与具体的截断无关),最后利用弱收敛性,通过取极限的方法证明了原问题解的存在性.The existence of the solution is discussed with u_0,v_0∈L_＋~4（Ω）,w∈W^（1,p）（Ω）（p≥2）.Firstly a regularization of the problem with u_0,v_0∈L_＋~∞（Ω） is made by a cut-off method.By compact lemma it is proved that the limit of the solutions of the regularized problem is a solution of the original problem after estimates.

关 键 词：退化抛物型方程 弱解 收敛性 GRONWALL引理 存在性 

分 类 号：O175.29[理学—数学]