The optimization method for solving a discrete inverse problem for a hyperbolic equation. (English. Russian original) Zbl 0960.65101
Dokl. Math. 58, No. 1, 32-35 (1998); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 361, No. 2, 154-157 (1998).
From the introduction: The optimization method is one of the most popular methods for solving inverse problems. We apply the optimization method to examine a discrete inverse problem. It is shown that the objective functional of the discrete inverse problem has only one stationary point, which coincides with the unique solution to the inverse problem.
MSC:
| 65M32 | Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs |
| 35K15 | Initial value problems for second-order parabolic equations |
| 35R30 | Inverse problems for PDEs |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
