越过临界状态的奇异扩散方程  

AN OVER CRITICAL SINGULAR DIFFUSION EQUATION

作　　者：潘佳庆[1] 

机构地区：[1]集美大学数学研究所,福建厦门361021

出　　处：《数学年刊（A辑）》2005年第3期427-434,共8页Chinese Annals of Mathematics

基　　金：福建省教育厅科技基金(No.JA03135)资助的项目.

摘　　要：本文讨论越过临界状态的奇异扩散方程Cauchy问题和带非线性边界条件的第二边值问题的可解性与不可解性.主要结果是: (1)若||u0||L1(R)<+∞,则对任意的正数T,方程的Cauchy问题在带型区域QT=R×(0,T)中不存在关于变量x为L1(R)可积的正解; (2)当且仅当T≤T0,矩形区域GT=(0,1)×(0,T)中的一类非线性边值问题存在唯一的经典解,其中T0=u0=integral from n=0 to1(u0(x)dx).In this paper, the solvability of the Cauchy problem and a kind of nonlinear boundary value problem for an over critical singular diffusion equation is discussed, the main results are that: (1) if ||u0||L1(R)<+∞,then for any positive number T, there is no positive L1 solution to the Cauchy problem in QT = R× (0, T); (2) there exists a unique classical positive smooth solution to this kind of nonlinear boundary value problem in GT = (0,1)×(0, T) if and only if T≤T0, where T0 = U0 =integral from n=0 to 1(u0(x)dx).

关 键 词：越过临界状态 CAUCHY问题 非线性边值问题 可解性 

分 类 号：O175.26[理学—数学]