Identification of the pollution source of a parabolic equation with the time-dependent heat conduction

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• 作者：Nguyen Huy Tuan (20) (21)
  Dang Duc Trong (21)
  Ta Hoang Thong (22)
  Nguyen Dang Minh (21)
  
  20. Saigon Institute for Computational Science and Technology ; Ho Chi Minh City ; Vietnam
  21. Department of Mathematics ; University of Natural Science ; Vietnam National University ; 227 Nguyen Van Cu ; Distric 5 ; Ho Chi Minh City ; Vietnam
  22. High School for the Gifted ; Vietnam National University ; Ho Chi Minh City ; Vietnam
  
• 刊名：Journal of Inequalities and Applications
• 出版年：2014
• 出版时间：December 2014
• 年：2014
• 卷：2014
• 期：1
• 全文大小：358 KB
• 参考文献：1. Atmadja, J, Bagtzoglou, AC (2003) Marching-jury backward beam equation and quasi-reversibility methods for hydrologic inversion: application to contaminant plume spatial distribution recovery. Water Resour. Res 39: pp. 1038-1047
  2. Cannon, JR, Duchateau, P (1998) Structural identification of an unknown source term in a heat equation. Inverse Probl 14: pp. 535-551 dx.doi.org/10.1088/0266-5611/14/3/010" target="_blank" title="It opens in new window">CrossRef
  3. Savateev, EG (1995) On problems of determining the source function in a parabolic equation. J. Inverse Ill-Posed Probl 3: pp. 83-102 dx.doi.org/10.1515/jiip.1995.3.1.83" target="_blank" title="It opens in new window">CrossRef
  4. Farcas, A, Lesnic, D (2006) The boundary-element method for the determination of a heat source dependent on one variable. J. Eng. Math 54: pp. 375-388 dx.doi.org/10.1007/s10665-005-9023-0" target="_blank" title="It opens in new window">CrossRef
  5. Johansson, T, Lesnic, D (2007) Determination of a spacewise dependent heat source. J. Comput. Appl. Math 209: pp. 66-80 dx.doi.org/10.1016/j.cam.2006.10.026" target="_blank" title="It opens in new window">CrossRef
  6. Yan, L, Fu, C-L, Yang, F-L (2008) The method of fundamental solutions for the inverse heat source problem. Eng. Anal. Bound. Elem 32: pp. 216-222 dx.doi.org/10.1016/j.enganabound.2007.08.002" target="_blank" title="It opens in new window">CrossRef
  7. Yang, F, Fu, C-L (2009) Two regularization methods for identification of the heat source depending only on spatial variable for the heat equation. J. Inverse Ill-Posed Probl 17: pp. 815-830 dx.doi.org/10.1515/JIIP.2009.048" target="_blank" title="It opens in new window">CrossRef
  8. Cheng, W, Fu, C-L (2013) Identifying an unknown source term in a spherically symmetric parabolic equation. Appl. Math. Lett 26: pp. 387-391 dx.doi.org/10.1016/j.aml.2012.10.009" target="_blank" title="It opens in new window">CrossRef
  9. Yang, F, Fu, C-L (2010) A simplified Tikhonov regularization method for determining the heat source. Appl. Math. Model 34: pp. 3286-3299 dx.doi.org/10.1016/j.apm.2010.02.020" target="_blank" title="It opens in new window">CrossRef
  10. Yang, F, Fu, C-L (2014) A mollification regularization method for the inverse spatial-dependent heat source problem. J.聽Comput. Appl. Math 255: pp. 555-567 dx.doi.org/10.1016/j.cam.2013.06.012" target="_blank" title="It opens in new window">CrossRef
  11. Trong, DD, Tuan, NH (2008) A nonhomogeneous backward heat problem: regularization and error estimates. Electron. J.聽Differ. Equ.
  12. Trong, DD, Quan, PH, Alain, PND (2006) Determination of a two dimensional heat source: uniqueness, regularization and error estimate. J. Comput. Appl. Math 191: pp. 50-67 dx.doi.org/10.1016/j.cam.2005.04.022" target="_blank" title="It opens in new window">CrossRef
  13. Qian, A, Li, Y (2011) Optimal error bound and generalized Tikhonov regularization for identifying an unknown source in the heat equation. J. Math. Chem 49: pp. 765-775 dx.doi.org/10.1007/s10910-010-9774-3" target="_blank" title="It opens in new window">CrossRef
  14. Hasanov, A (2012) Identification of spacewise and time dependent source terms in 1D heat conduction equation from temperature measurement at a final time. Int. J. Heat Mass Transf 55: pp. 2069-2080 dx.doi.org/10.1016/j.ijheatmasstransfer.2011.12.009" target="_blank" title="It opens in new window">CrossRef
  15. Denche, M, Bessila, K (2005) A modified quasi-boundary value method for ill-posed problems. J. Math. Anal. Appl 301: pp. 419-426 dx.doi.org/10.1016/j.jmaa.2004.08.001" target="_blank" title="It opens in new window">CrossRef
  
• 刊物主题：Analysis; Applications of Mathematics; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1029-242X

文摘

We consider the problem of identifying the pollution source of a 1D parabolic equation from the initial and the final data. The problem is ill posed and regularization is in order. Using the quasi-boundary method and the truncation Fourier method, we present two regularization methods. Error estimates are given and the methods are illustrated by numerical experiments.