一类非线性方程解的blow up及局部迭代解  

THE BLOW UP SOLUTION AND LOCALLY INTERATIVE SOLUTION OF THE FIRST KIND NON-LINEAR EQUATION

作　　者：李文深[1] 王劲书 

机构地区：[1]东北林业大学 [2]哈尔滨木器厂

出　　处：《东北林业大学学报》1992年第4期80-88,共9页Journal of Northeast Forestry University

摘　　要：本文以一种变换。化非线性方程为非线性抛物型方程,并利用凸性方法及最大值原理证明其初边值问题的解于有限时间内blow up. 然后借助于Riemann函数。设计一结构,由此经积分而变原问题为积分微分方程,再依不动点原理证明它与原问题等价,且由该积分微分方程而求得一致收敛的迭代解。The paper changes the non-linear equation into a non-linear parabolic equation by a kind of change and proves the blow up of solution of its initial boundary value problem in finite time by using convexity method and maximum principle.Then,designing a structure by way of Riemann function, it changes the original problem into an integral and differential equation through integral, proves them equivalent according to fixed-point theorem, and gets the uniformly convergent interative solution on the basis of integral and differential equation.

关 键 词：非线性方程 局部迭代解 

分 类 号：O175.14[理学—数学]