| 一维非线性伪抛物方程的逼近解 |
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| 引用本文： | 周世平,崔明根.一维非线性伪抛物方程的逼近解[J].黑龙江大学自然科学学报,2009,26(6). |
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| 作者姓名： | 周世平 崔明根 |
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| 作者单位： | 1. 哈尔滨工业大学(威海)数学系,威海,264209;烟台大学,计算机学院,烟台,264005
2. 哈尔滨工业大学(威海)数学系,威海,264209 |
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| 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u_n(x,t)收敛于真解u(x,t),且u_n(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,u_n(x,t)是最佳逼近解.
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| 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 |
Approximate solution for one-dimensional nonlinear pseudoparabolic equation |
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| ZHOU Shi-ping,CUI Ming-gen.Approximate solution for one-dimensional nonlinear pseudoparabolic equation[J].Journal of Natural Science of Heilongjiang University,2009,26(6). |
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| Authors: | ZHOU Shi-ping CUI Ming-gen |
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| Abstract: | An iterative method is given to solve one-dimensional nonlinear pseudoparabolic equation in the reproducing space. It is proved that the approximate sequence u_n(x, t) converges to the exact solution u(x,t). Moreover, the partial derivatives of u_n(x,t) are also convergent to the partial derivatives of u(x, t). And the approximate sequence u_n(x, t) is the best approximation under a complete normal orthogonal system. |
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| Keywords: | approximate solution nonlinear pseudoparabolic equation reproducing kernel space nonlocal boundary condition |
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