中文摘要：

考虑了一类利用终端观测值反演热传导方程中源项系数的反问题，此类问题无论是在理论讨论还是在实际应用中都有极其重要的研究意义。基于最优控制框架下讨论了控制泛函极小元的存在性及其满足的必要条件，最后证明了最优解的唯一性及稳定性。

英文摘要：

This paper studies an inverse problem of identifying the source term coefficient in a class of heat conduction equations from the final observation, which is of great significance both in theory and practice. Based on the optimal control framework, the existence of the minimizer and the necessary conditions are deduced. At the end of the paper, the uniqueness and the stability of the solution are also proved.