Determine the special term of a two-dimensional heat source

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.

Keywords:

• heat source
• ill-posed problem
• interpolation method
• Fourier series

AMS Subject Classification::

• 35K05

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.