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| 求解一类反向热传导问题的Fourier正则化和Tikhonov正则化方法 | |
| 引用本文： | 张军勇,高翔,傅初黎.求解一类反向热传导问题的Fourier正则化和Tikhonov正则化方法[J].兰州大学学报(自然科学版),2007,43(2):112-116. |
| 作者姓名： | 张军勇 高翔 傅初黎 |
| 作者单位： | 1. 兰州大学,数学与统计学院,甘肃,兰州,730000;北京应用物理与计算数学研究所,北京,100088 2. 兰州大学,数学与统计学院,甘肃,兰州,730000;天水师范学校,数学系,甘肃,天水,741000 3. 兰州大学,数学与统计学院,甘肃,兰州,730000 |
| 基金项目： | 国家自然科学基金，甘肃省自然科学基金，兰州大学校科研和教改项目 |
| 摘 要： | 讨论了一类一维反向热传导问题,利用Fourier正则化方法给出了正则近似解,得到了H(o)lder型误差估计.同时通过提高先验光滑性假设,并利用Tikhonov正则化方法得到了对数型稳定性估计,解决了零点的收敛性问题. |
| 关 键 词： | 反向热传导 不适定问题 Fourier正则化 Tikhonov正则化 误差估计 |
| 文章编号： | 0455-2059（2007）02-0112-05 |
| 修稿时间： | 2005-06-212006-04-25 |
Fourier and Tikhonov regularization methods for solving a class of backward heat conduction problems |
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| ZHANG Jun-yong,GAO Xiang,FU Chu-li.Fourier and Tikhonov regularization methods for solving a class of backward heat conduction problems[J].Journal of Lanzhou University(Natural Science),2007,43(2):112-116. | |
| Authors: | ZHANG Jun-yong GAO Xiang FU Chu-li |
| Institution: | 1. School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China; 2. Institute of Applied Physics and Computational Mathematics, Beijing 100088, China; 3. Department of Mathematics, Tianshui Normal School, Tianshui 741000, Gansu, China |
| Abstract: | A class of one-dimensional backward heat conduction problems are discussed and a Fourier regularization approximating solution with HSlder type stability estimate is given. Moreover, by improving the a priori assumption, a Tikhonov regularization approximating solution with logarithmic type stability estimate is also given and the convergence of the solution at t =0 is proved. |
| Keywords: | backward heat conduction ill-posed problem Fourier regularization Tikhonov regularization error estimate |
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