非线性抛物型方程反问题的一种新算法  

A New Numerical Method for Inverse Problems of Nonlinear Parabolic Equations

作　　者：何杰[1] 徐定华[1] 张文[1] 

机构地区：[1]东华理工大学数学与信息科学学院,江西抚州344000

出　　处：《东华理工学院学报》2007年第2期196-200,共5页Journal of East China Institute of Technology

基　　金：国家自然科学基金(10561001);江西省自然科学基金(0511005);东华理工大学校长基金(DHXK0701)

摘　　要：利用反问题新算法—时间域正演反演法研究非线性抛物型方程的逆时反问题。该方法处理反问题的主要思路是先求解相对应的正问题,获得解在特定时间网格处的近似值;然后构造一个合适的全纯映射,在象空间中获得解在时间网格对应点处的近似值;最后利用解析函数的唯一延拓性质实现反问题的逆时间反演。数值模拟例子说明了方法的有效性。An inverse problem for backward nonlinear parabolic equations is investigated. The inverse problem is solved by a new problem-solving approach, forward-backward algorithm in time domain. At first, the corresponding forward problem is discussed, and its approximate value is obtained in specific time grid. Then a suitable holomorphic mapping is constructed, and the corresponding approximate value is obtained in image space. Finally, the backward inversion of the inverse problem is realized by the uniqueness of analytic extension. And the numerical example demonstrates that the given method is effective.

关 键 词：非线性抛物型方程 反问题 时间域正演反演算法 全纯映射 数值算法 

分 类 号：O175.26[理学—数学]