A procedure for determining a spacewise dependent heat source and the initial temperature

International Journal of Phytoremediation

Volumn 87, Issue 3, 2008, Pages 265-276

  Johansson, B Tomas ^a   Lesnic, Daniel ^b  

^a UNIVERSITY OF BIRMINGHAM   (United Kingdom)

^b UNIVERSITY OF LEEDS   (United Kingdom)

Author keywords

Boundary element method; Discrepancy principle; Heat source; Initial condition; Inverse problem; Iterative regularization; Parabolic heat equation

Indexed keywords

EID: 55549142572     PISSN: 15226514     EISSN: 15497879     Source Type: Journal    
DOI: 10.1080/00036810701858193     Document Type: Article

References (14)

1. Cannon, JR. 1966. “ Some numerical results for the solution of the heat equation backwards in time ”. In Numerical Solutions of Nonlinear Differential Equations, Edited by: Greenspan, D. 21–54. New York: J. Wiley.
2. Colton, D. 1979. The approximation of solutions to the backwards heat equation in a nonhomogeneous medium. J. Math. Anal. Appl., 72: 418–429.
3. Lattès, R, and Lions, J-L. 1969. The Method of Quasi-Reversibility, Applications to Partial Differential Equations, New York: American Elsevier Publishing Co.
4. Mera, NS, Elliott, L, Ingham, DB, and Lesnic, D. 2001. An iterative boundary element method for solving the one-dimensional backward heat conduction problem. Inter. J. Heat Mass Transfer, 44: 1937–1946.
5. Cannon, JR. 1968. Determination of an unknown heat source from overspecified boundary data. SIAM J. Numer. Anal., 5: 275–286.
6. Prilepko, AI, and Solov'ev, VV. 1988. Solvability theorems and Rothe's method for inverse problems for a parabolic equation. Diff. Equat., 23: 1341–1349.
7. Solov'ev, VV. 1990. Solvability of the inverse problems of finding a source, using overdetermination on the upper base for a parabolic equation. Diff. Equat., 25: 1114–1119.
8. Johansson, T, and Lesnic, D. 2007. Determination of a spacewise dependent heat source. J. Comput. Appl. Math., 209: 66–80.
9. Bastay, G. 1995. Iterative Methods for Ill-posed Boundary Value Problems Linköping Studies in Science and Technology, Dissertations No. 392, Linköping Univ., Linköping
10. Rundell, W. 1980. Determination of an unknown non-homogeneous term in a linear partial differential equation from overspecified boundary data. Appl. Anal., 10: 231–242.
11. Lions, J-L, and Magenes, E. 1972. Non-homogeneous Boundary Value Problems and Applications, Vol. I, Berlin: Springer-Verlag.
12. Engl, HW, Hanke, M, and Neubauer, A. 1996. Regularization of Inverse Problems, Dordrecht: Kluwer Academic Publishers Group.
13. Morozov, VA. 1966. On the solution of functional equations by the method of regularization. Doklady Akad. Nauk SSSR, 167: 510–512. English transl.: Soviet Mathematics Doklady, 7 (1966), 414–417
14. Farcas, A, and Lesnic, D. 2006. The boundary-element method for the determination of a heat source dependent on one variable. J. Eng. Math., 54: 375–388.