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- 2016
一类Kolmogorov型方程的系数反演问题
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Abstract:
摘要： 研究了一类Kolmogorov型方程的对流系数反演问题,这类问题在很多科学研究和工程领域都有重要的应用,其特点是未知系数是同时依赖于空间变量x和时间变量t的函数。基于最优控制理论框架下,先将原问题转化为一个优化问题,并证明了控制泛函最优解的存在性及它满足的必要条件,然后证明了最优解的稳定性和唯一性。
Abstract: This work investigates an inverse problem of reconstructing the convection coefficient in a Kolmogorov equation from the final measurement data, which has important application in many fields of applied science. Compared with ordinary inverse problems, the unknown coefficient in this work depends on both the space variable x and the time variable t. On the basis of the optimal control framework, the identification problem is transformed into an optimization problem and the existence of the minimizer for the cost functional is established. Then necessary condition of the minimizer is obtained. After the necessary condition of the minimizer satisfied, the stability and uniqueness of the minimizer are deduced
| [1] | DENG Zuicha, YANG Liu, YU Jianning, et al. Identifying the radiative coefficient of an evolutional type heat conduction equation by optimization method[J]. J Math Anal Appl, 2010, 362(1):210-223. |
| [2] | MA Yunjie, FU Chuli, ZHANG Yuanxiang. Identification of an unknown sourse depending on both time and space variables by a variational method[J]. Appl Math Model, 2012, 36:5080-5090. |
| [3] | 姜礼尚. 金融衍生产品定价的数学模型与案例分析[M]. 北京: 高等教育出版社, 2008. JIANG Lishang. Mathematical models and case analysis in financial derivetives pricing[M]. Beijing: Higher Education Press, 2008. |
| [4] | 姜礼尚. 期权定价的数学模型与方法[M]. 北京: 高等教育出版社, 2003. JIANG Lishang. Mathematical models and methods for option pricing[M]. Beijing: Higher Education Press, 2003. |
| [5] | ZHAO Xiaofeng, HUANG Sixun, KANG Linchun. New method to solve electromagnetic parabolic equation[J]. Appl Math Mech, 2013, 34(11):1373-1382. |
| [6] | WEI Ting, WANG Jungang. A modified quasi-boundary value method for an inverse source problem of the time-fractional diffusion equation[J]. Appl Numer Math, 2014, 78:95-111. |
| [7] | YANG Fan, FU Chuli. A mollification regularization method for the inverse spatial-dependent heat source problem[J]. J Comput Appl Math, 2014, 255:555-567. |
| [8] | SAKAMOTO K, YAMAMOTO M. Inverse heat source problem from time distributing overdetermination[J]. Appl Anal, 2009, 88(5):735-748. |
| [9] | YANG Liu, DEHGHAN M, YU Jianning, et al. Inverse problrem of time-dependent heat sources numerical reconstruction[J]. Math and Comp in Simul, 2011, 81:1656-1672. |
| [10] | KOSTIN A B. The inverse problem of recovering the source in a parabolic equation under a condition of nonlocal observation[J]. Sbornik: Mathematics, 2013, 204(10):1391-1434. |
| [11] | JIANG Daijun, FENG Hui, ZOU Jun. Convergence rates of Tikhonov regularizations for parameter identification in a parabolic-elliptic system[J]. Inverse Problems, 2012, 28(10), 104002(20pp). |
| [12] | YANG Liu, YU Jianning, DENG Zuicha. An inverse problrem of identifying the coefficient of parabolic equation[J]. Appl Math Model, 2008, 32:1984-1995. |
| [13] | DENG Zuicha, YANG Liu. An inverse problrem of identifying the radiative coefficient in a degenerate parabolic equation[J]. Chin Annal Math, 2014, 35B(3):355-382. |
