A NEW METHOD FOR REGULARIZING A HEAT INVERSE PROBLEM WITH TIME DEPENDENT COEFFICIENT IN THE TWO-DIMENSIONAL CASE
DOI:
https://doi.org/10.18173/2354-1059.2024-0002Keywords:
heat inverse problem, regularization, truncation method, quasi-boundary value methodAbstract
In this paper, we consider an inverse problem with a time-dependent coefficient. This problem is ill-posed. To regularize this problem, we use the integral truncation method combined with the quasi-boundary value method. We construct approximate solutions and consider the stability of such a solution. Moreover, we evaluate the errors between regularized solutions and exact solutions. A numerical method is given to illustrate the theoretically obtained results.
References
[1] Lattes R & Lions JL, (1967), Methode de Quasi-Reversibilite et Applications, Dunod, Paris.
[2] Clark G & Oppenheimer C, (1994), Quasi-reversibility methods for non-well posed problem. Electronic Journal of Differential Equations, 8, 1-9.
[3] Denche M & Bessila K, (2001), Quasi-boundary value method for non-well posed problems for a parabolic equation with integral boundary condition. Mathematical Problems in Engineering, 7(2), 129-145.
[4] Denche M & Bessila K, (2005), A modifed quasi-boundary value method for ill-posed problems. Journal of Mathematical Analysis and Applications, (301), 419-426.
[5] Pham HQ, Dang DT, Le MT & Nguyen HT, (2011), A modifed quasi – boundary value method for regularizing of a backward problem with time-dependent coeffcient. Inverse Problems in Science and Engineering, 19(3), 409-423.
[6] Nguyen HT, Pham HQ, Dang DT & Le MT, (2013), On a backward heat problem with time-dependent coeffcicent: Regularization and error estimates. Applied Mathematics and Computation, 219, 6066-6073.
[7] Kirsch A, (1966), An introduction to the mathematical theory of inverse problem, Springer
