Abstract
We consider the problem of determining a pair of functions (u, f) satisfying the heat equation , where and the function ϕ is given. The problem is ill-posed. Under a slight condition on ϕ, we show that the solution is determined uniquely from some boundary data and the initial temperature. Using the interpolation method and the truncated Fourier series, we construct a regularized solution of the source term f from non-smooth data. The error estimate and numerical experiments are given.
AMS Subject Classification::
Acknowledgements
The authors would like to thank the referee for valuable suggestions leading to the improved version of this article. Our thanks also go to Phung Trong Thuc for his help in correcting errata.