| 具有未知源的某些非线性伪抛物型方程的反问题 |
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| 引用本文： | 江成顺,孙同军.具有未知源的某些非线性伪抛物型方程的反问题[J].数学研究,1999,32(2):116-124. |
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| 作者姓名： | 江成顺 孙同军 |
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| 作者单位： | 信息工程学院应用数学系!郑州450052(江成顺)，山东大学数学学院博士后信箱!济南250100(孙同军) |
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| 摘 要： | 考 虑具有未 知源项的 某些非 线性伪 抛物 型方程 的反演 问题． 首先 将伪抛 物型 方程初 边值问 题化为非线 性发展方 程 Ｃｏｕｃｈ ｙ 问题，然 后，利用半 群理论，论 证发展 方程反问 题解的存 在唯一 性，最后， 利用不 动点方法得到 伪抛物型方程反 问题的可解性
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| 关 键 词： | 伪抛物型方程 反问题 发展方程 半群理论 不动点方法 |
Inverse Problem for Some Nonlinear Pseudo Parabolic Equations with Unknown Source |
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| Jiang Chengshun.Inverse Problem for Some Nonlinear Pseudo Parabolic Equations with Unknown Source[J].Journal of Mathematical Study,1999,32(2):116-124. |
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| Authors: | Jiang Chengshun |
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| Abstract: | This paper deals with an inverse problem for some nonlinear pseudo parabolic equations with their unknown source terms. Firstly, the authors change the initial boundary value problem for pseudo parabolic equations into Cauchy problem of the nonlinear evolution equations. Secondly, by using the semigroup theory, the authors establish the existence and uniqueness of solutions of the inverse problem for the evolution equations. Finally, they take advantage of the fixed point method for some contraction mapping and get the solvability of the inverse problem of the inverse problem of the pseudo parabolic equations. |
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| Keywords: | pseudo parabolic equation inverse problem evolution equation semigroup theory fixed point method |
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