关于一类热传导方程的间断扩散系数的稳定方法

Stable Method for Discontinuous Diffusion Coefficient in Class of Heat Conduction Equations

考虑了一类利用终端观测值反演热传导方程中间断扩散系数的反问题,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。相较于扩散系数连续的文献,间断的情形鲜有文献涉足,由于控制泛函非凸,一般来说没有唯一性,在假设T比较小的情况下,证明了极小元的唯一性和稳定性。

This paper studies an inverse problem of identifying the discontinuous diffusion coefficient in a class of heat conduction equations from the final observation,which is of great significance both in theory and practice. Being different from ordinary continuous diffusion coefficient problems,documents concerned the discontinuous case are rather few. Since the control functional is non-convex,the uniqueness of the optimal solution can not be guaranteed. Assuming that T is relatively small,it is proved that the minizer is unique and stable.