半线性抛物型方程初边值问题解的性态  

The Behavior of Solution of Initial Boundary Value Problem for Semi-linear Parabolic Equation

作　　者：容跃堂[1] 荔炜[2] 

机构地区：[1]西北纺织工学院 [2]西北大学

出　　处：《纯粹数学与应用数学》1992年第2期21-26,共6页Pure and Applied Mathematics

摘　　要：1.引言对于半线性抛物型议程的初边值问题■解的性质有许多作者进行了讨论,设λ_0是-T(D(x)T)所对应的最小特征值,φ(x)为对应的特征函数,则λ_0>0,且可取φ(x)>0。Consider the initial boundary value problem for semi--linear parabolic equation Then the property of blow up depend not only λ,but also function f(t). Suppose f(t)>0 and f (t)=O(e~?), if α(λ--λ_0)+β<0,then the solution blow up for big inital data and global solution exists forsmall data. When u_0(x)≥0 is bounded above, in order to exist a global solution, it is sufficient to takeβsmall, f(t) is a factor to avoid blow up.

关 键 词：抛物型方程 初边值问题 解 半线性 

分 类 号：O175.26[理学—数学]