A backward parabolic equation with a time-dependent coefficient: regularization and error estimates. (English) Zbl 1263.65091
The paper considers the backward parabolic equation with time-dependent coefficients in one space dimension. Based on an analytic formula of the exact solution, a regularized solution is proposed. Under suitable conditions for the exact solution, an error estimate between the exact solution and the regularized solution is proved. Numerical results are provided.
Reviewer: Zhiming Chen (Beijing)
MSC:
| 65M30 | Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs |
| 35K05 | Heat equation |
| 35R25 | Ill-posed problems for PDEs |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
