非线性发展方程解的渐近性的构造过程

A Constructive Approach on the Asymptotic Behavior of Solutions of Nonlinear Evolution Equations

本文借助Banach空间中的新不等式,通过迭代过程x_(n+1)=x_n—a_nAx_n(x_0∈D(A),n=0,1,2,…)研究非线性发展方程du/dt=—Au解的渐近性,构造性地证明了,在一定条件下{x_n}的极限点就是该发展方程的平衡点,推广了文献[1]的结论。

A new inequality of Banach space and the iterative process D(A),n = 0,1,2 ,---,' are used to research the asymptotic behavior of solutions of Au. It is proved that the limit of the sequence {xn} is just the equilibrium point of the equation. The conclusions generalize those in [1].