A regularization method for solving the radially symmetric backward heat conduction problem. (English) Zbl 1524.65325
Summary: This work is devoted to solving the radially symmetric backward heat conduction problem, starting from the final temperature distribution. The problem is ill-posed: the solution (if it exists) does not depend continuously on the given data. A modified Tikhonov regularization method is proposed for solving this inverse problem. A quite sharp estimate of the error between the approximate solution and the exact solution is obtained with a suitable choice of regularization parameter. A numerical example is presented to verify the efficiency and accuracy of the method.
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65M30 | Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs |
| 35R25 | Ill-posed problems for PDEs |
| 35K05 | Heat equation |
| 35R30 | Inverse problems for PDEs |
| 65M32 | Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 35Q79 | PDEs in connection with classical thermodynamics and heat transfer |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 65J20 | Numerical solutions of ill-posed problems in abstract spaces; regularization |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 65K10 | Numerical optimization and variational techniques |
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