| 一类非线性伪抛物型方程混合问题古典解的存在唯一性 |
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| 引用本文： | 刘 勃,宋惠元.一类非线性伪抛物型方程混合问题古典解的存在唯一性[J].信息工程大学学报,2005,6(2):35-38. |
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| 作者姓名： | 刘 勃 宋惠元 |
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| 作者单位： | 信息工程大学,信息工程学院,河南,郑州,450002 |
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| 摘 要： | 文章讨论了一类非线性伪抛物型方程的混合问题。首先通过积分变换，将问题的左端项简化成线性算子，然后利用该算子的Riemann函数构造一个辅助问题，得到了与原问题．等价的积分微分方程，最后利用不动点理论证明了这个积分微分方程存在唯一古典解。从而得到了所述混合问题的可解性。
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| 关 键 词： | 非线性伪抛物型方程 积分微分方程 Riemann方法 不动点理论 |
| 文章编号： | 1671-0673(2005)02-0035-04 |
| 修稿时间： | 2004年6月11日 |
Classical Solution to Mixed Problem for Some Nonlinear Pseudo-Parabolic Partial Equations |
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| LIU Bo,SONG Hui-yuan.Classical Solution to Mixed Problem for Some Nonlinear Pseudo-Parabolic Partial Equations[J].Journal of Information Engineering University,2005,6(2):35-38. |
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| Authors: | LIU Bo SONG Hui-yuan |
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| Affiliation: | Institute of Information Engineering, Information Engineering University, Zhengzhou, 450002, China |
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| Abstract: | The aim of this paper is to investigate mixed problem for some nonlinear pseudo-parabolic partial equations. Firstly, the left side of the equation is turned into a linear operator. Then by using the Riemann's function of the operator to construct an auxiliary problem, an integrodifferential equation equivalent to former problem is obtained. Finally, based on fixed point theory, the existence and uniqueness of the classical solution to the integrodifferential equation is proved. That is, there is one and only one classical solution for the nonlinear pseudo-parabolic equation. |
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| Keywords: | nonlinear pseudo-parabolic partial equation integrodifferential equation Riemann's function fixed point theory |
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