夹逼准则与抛物型偏微分方程的上下解方法

The Squeeze Theorem and the Upper-lower Solution Methods for Parabolic Partial Defferential Equation

文章把极限的夹逼准则思想应用到抛物型偏微分方程,通过引进上下解,构造出一串单调非增的上解序列和一串单调非减的下解序列,证明了半线性抛物型偏微分方程初边值问题解存在的唯一性。

The paper applies the criteria for limit squeezing principle to parabolic partial differential equations. Through the introduction of upper and lower solution,a string of non-monotonous sequence of solution and a string of non-monotonous solution by the next sequence are constructed, which proves the unique existence of the solution of semi-linear parabolic partial differential equation boundary value problems.