一维非线性伪抛物方程的逼近解(英文)  

Approximate solution for one-dimensional nonlinear pseudoparabolic equation

作　　者：周世平[1,2] 崔明根[1] 

机构地区：[1]哈尔滨工业大学(威海)数学系,威海264209 [2]烟台大学计算机学院,烟台264005

出　　处：《黑龙江大学自然科学学报》2009年第6期711-717,共7页Journal of Natural Science of Heilongjiang University

摘　　要：探讨在再生核空间用迭代法求解一维非线性伪抛物方程。证明逼近解un(x,t)收敛于真解u(x,t),且un(x,t)的各阶偏导数亦收敛于u(x,t)相应阶的偏导数。在一个完全标准正交系下,un(x,t)是最佳逼近解。An iterative method is given to solve one-dimensional nonlinear pseudoparabolic equation in the reproducing space. It is proved that the approximate sequence un （x, t） converges to the exact solution u （x, t）. Moreover, the partial derivatives of un （x, t） are also convergent to the partial derivatives of u（x, t）. And the approximate sequence uo （x, t） is the best approximation under a complete normal orthogonal system.

关 键 词：逼近解 非线性伪抛物方程 再生核空间 非局部边值条件 

分 类 号：O189.1[理学—数学]