| 一非线性发展方程的反问题 |
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| 引用本文： | 江成顺,崔国忠,孙同军.一非线性发展方程的反问题[J].数学研究及应用,2001,21(1):53-59. |
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| 作者姓名： | 江成顺 崔国忠 孙同军 |
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| 作者单位： | 1. 信息工程大学应用数学系,
2. 山东大学数学学院, |
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| 基金项目： | Supported by the Post-doctorate Science Foundation and the National NSF of China |
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| 摘 要： | 研究一非线性发展方程的未知源项的反演问题.首先，把所考虑的初边值问题化成一等价非线性发展方程的Cauchy问题；然后，利用半群理论，论证反问题解的存在性和唯一性；最后，利用压缩映射不动点方法，得到反问题的可解性.
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| 关 键 词： | 非线性发展方程 反问题 初边值问题 CAUCHY问题 |
| 文章编号： | 1000-341X(2001)01-0053-07 |
| 收稿时间： | 1998/3/10 0:00:00 |
| 修稿时间： | 1998年3月10日 |
An Inverse Problem for a Nonlinear Evolution Equation |
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| JIANG Cheng-shun,CUI Guo-zhong and SUN Tong-jun.An Inverse Problem for a Nonlinear Evolution Equation[J].Journal of Mathematical Research with Applications,2001,21(1):53-59. |
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| Authors: | JIANG Cheng-shun CUI Guo-zhong and SUN Tong-jun |
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| Affiliation: | Dept. of Appl. Math., Univ. of Information Engineering, Zhengzhou 450002, China;Dept. of Appl. Math., Univ. of Information Engineering, Zhengzhou 450002, China;Inst. of Math., Shandong University, Jinan 250100, China |
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| Abstract: | This paper deals with an inverse problem for the unknown source term in a nonlinear evolution equation. Firstly, the authors change the initial boundary value problem (IBVP) for the equation into a Cauchy problem for a certain nonlinear evolution equation. Secondly, using the semigroup theory, the authors establish the existence and uniqueness of the solution for the inverse problem. Finally, they take advantage of the fixed point method for some contraction mapping and get the solvability of the inverse problem for the evolution equation. |
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| Keywords: | evolution equation inverse problem semigroup theory fixed pointmethod |
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