Open Science Research Excellence

Open Science Index

Commenced in January 2007 Frequency: Monthly Edition: International Publications Count: 29725

Select areas to restrict search in scientific publication database:
Identifying an Unknown Source in the Poisson Equation by a Modified Tikhonov Regularization Method
In this paper, we consider the problem for identifying the unknown source in the Poisson equation. A modified Tikhonov regularization method is presented to deal with illposedness of the problem and error estimates are obtained with an a priori strategy and an a posteriori choice rule to find the regularization parameter. Numerical examples show that the proposed method is effective and stable.
Digital Object Identifier (DOI):


[1] A. Burykin, A. Denisov, Determination of the unknown sources in the heat-conduction equation, Computational Mathematics and Modeling 8 (4) (1997) 309-313.
[2] J. Cannon, P. Duchateau, Structural identification of an unknown source term in a heat equation, Inverse Problems 14 (3) (1998) 535-551.
[3] J. Cannon, S. Perez-Esteva, Uniqueness and stability of 3d heat sources, Inverse problems 7 (1991) 57.
[4] M. Choulli, M. Yamamoto, Conditional stability in determining a heat source, Journal of Inverse and Ill-posed Problems 12 (3) (2004) 233-243.
[5] F. Dou, C. Fu, F. Yang, Optimal error bound and Fourier regularization for identifying an unknown source in the heat equation, Journal of Computational and Applied Mathematics 230 (2) (2009) 728-737.
[6] A. El Badia, T. Ha-Duong, On an inverse source problem for the heat equation. Application to a pollution detection problem, Journal of Inverse and Ill-posed Problems 10 (6) (2002) 585-600.
[7] A. Farcas, D. Lesnic, The boundary-element method for the determination of a heat source dependent on one variable, Journal of Engineering Mathematics 54 (4) (2006) 375-388.
[8] A. Kirsch, An introduction to the mathematical theory of inverse problems, Springer-Verlag,New York, 1996.
[9] G. Li, Data compatibility and conditional stability for an inverse source problem in the heat equation, Applied Mathematics and Computation 173 (1) (2006) 566-581.
[10] L. Ling, M. Yamamoto, Y. Hon, T. Takeuchi, Identification of source locations in two-dimensional heat equations, Inverse Problems 22 (4) (2006) 1289-1305.
[11] H. Park, J. Chung, A sequential method of solving inverse natural convection problems, Inverse Problems 18 (3) (2002) 529-546.
[12] V. Ryaben'kii, S. Tsynkov, S. Utyuzhnikov, Inverse source problem and active shielding for composite domains, Applied Mathematics Letters 20 (5) (2007) 511-515.
[13] M. Yamamoto, Conditional stability in determination of force terms of heat equations in a rectangle, Mathematical and Computer Modelling 18 (1) (1993) 79-88.
[14] L. Yan, C. Fu, F. Yang, The method of fundamental solutions for the inverse heat source problem, Engineering Analysis with Boundary Elements 32 (3) (2008) 216–222.
[15] L. Yan, F. Yang, C. Fu, A meshless method for solving an inverse spacewise-dependent heat source problem, Journal of Computational Physics 228 (1) (2009) 123–136.
[16] F. Yang, The truncation method for identifying an unknown source in the poisson equation, Applied Mathematics and Computation 22 (2011) 9334–9339.
[17] F. Yang, C. Fu, The modified regularization method for identifying the unknown source on poisson equation, Applied Mathematical Modelling 2 (2012) 756–763.
[18] Z. Yi, D. Murio, Source term identification in 1-D IHCP, Computers & Mathematics with Applications 47 (12) (2004) 1921–1933.
[19] Z. Zhao, Z. Meng, A modified tikhonov regularization method for a backward heat equation, Inverse Problems in Science and Engineering 19 (8) (2011) 1175–1182.
Vol:13 No:06 2019Vol:13 No:05 2019Vol:13 No:04 2019Vol:13 No:03 2019Vol:13 No:02 2019Vol:13 No:01 2019
Vol:12 No:12 2018Vol:12 No:11 2018Vol:12 No:10 2018Vol:12 No:09 2018Vol:12 No:08 2018Vol:12 No:07 2018Vol:12 No:06 2018Vol:12 No:05 2018Vol:12 No:04 2018Vol:12 No:03 2018Vol:12 No:02 2018Vol:12 No:01 2018
Vol:11 No:12 2017Vol:11 No:11 2017Vol:11 No:10 2017Vol:11 No:09 2017Vol:11 No:08 2017Vol:11 No:07 2017Vol:11 No:06 2017Vol:11 No:05 2017Vol:11 No:04 2017Vol:11 No:03 2017Vol:11 No:02 2017Vol:11 No:01 2017
Vol:10 No:12 2016Vol:10 No:11 2016Vol:10 No:10 2016Vol:10 No:09 2016Vol:10 No:08 2016Vol:10 No:07 2016Vol:10 No:06 2016Vol:10 No:05 2016Vol:10 No:04 2016Vol:10 No:03 2016Vol:10 No:02 2016Vol:10 No:01 2016
Vol:9 No:12 2015Vol:9 No:11 2015Vol:9 No:10 2015Vol:9 No:09 2015Vol:9 No:08 2015Vol:9 No:07 2015Vol:9 No:06 2015Vol:9 No:05 2015Vol:9 No:04 2015Vol:9 No:03 2015Vol:9 No:02 2015Vol:9 No:01 2015
Vol:8 No:12 2014Vol:8 No:11 2014Vol:8 No:10 2014Vol:8 No:09 2014Vol:8 No:08 2014Vol:8 No:07 2014Vol:8 No:06 2014Vol:8 No:05 2014Vol:8 No:04 2014Vol:8 No:03 2014Vol:8 No:02 2014Vol:8 No:01 2014
Vol:7 No:12 2013Vol:7 No:11 2013Vol:7 No:10 2013Vol:7 No:09 2013Vol:7 No:08 2013Vol:7 No:07 2013Vol:7 No:06 2013Vol:7 No:05 2013Vol:7 No:04 2013Vol:7 No:03 2013Vol:7 No:02 2013Vol:7 No:01 2013
Vol:6 No:12 2012Vol:6 No:11 2012Vol:6 No:10 2012Vol:6 No:09 2012Vol:6 No:08 2012Vol:6 No:07 2012Vol:6 No:06 2012Vol:6 No:05 2012Vol:6 No:04 2012Vol:6 No:03 2012Vol:6 No:02 2012Vol:6 No:01 2012
Vol:5 No:12 2011Vol:5 No:11 2011Vol:5 No:10 2011Vol:5 No:09 2011Vol:5 No:08 2011Vol:5 No:07 2011Vol:5 No:06 2011Vol:5 No:05 2011Vol:5 No:04 2011Vol:5 No:03 2011Vol:5 No:02 2011Vol:5 No:01 2011
Vol:4 No:12 2010Vol:4 No:11 2010Vol:4 No:10 2010Vol:4 No:09 2010Vol:4 No:08 2010Vol:4 No:07 2010Vol:4 No:06 2010Vol:4 No:05 2010Vol:4 No:04 2010Vol:4 No:03 2010Vol:4 No:02 2010Vol:4 No:01 2010
Vol:3 No:12 2009Vol:3 No:11 2009Vol:3 No:10 2009Vol:3 No:09 2009Vol:3 No:08 2009Vol:3 No:07 2009Vol:3 No:06 2009Vol:3 No:05 2009Vol:3 No:04 2009Vol:3 No:03 2009Vol:3 No:02 2009Vol:3 No:01 2009
Vol:2 No:12 2008Vol:2 No:11 2008Vol:2 No:10 2008Vol:2 No:09 2008Vol:2 No:08 2008Vol:2 No:07 2008Vol:2 No:06 2008Vol:2 No:05 2008Vol:2 No:04 2008Vol:2 No:03 2008Vol:2 No:02 2008Vol:2 No:01 2008
Vol:1 No:12 2007Vol:1 No:11 2007Vol:1 No:10 2007Vol:1 No:09 2007Vol:1 No:08 2007Vol:1 No:07 2007Vol:1 No:06 2007Vol:1 No:05 2007Vol:1 No:04 2007Vol:1 No:03 2007Vol:1 No:02 2007Vol:1 No:01 2007