热传导反问题（Inverse Heat Conduction Problems）在现代科学技术与工程领域有着广泛的应用背景，如热流、遥感技术、信号处理、连续介质力学及工业控制等领域，因而吸引了诸多的研究人员从事该领域方面的研究工作。由于外部测量数据不可避免的带有噪声误差，在Hadamard意义下热传导反问题是不适定的，即给数据较小的扰动会造成数值解很大的变化，也就不能保证待求解的稳定性，因此寻找一种稳定的数值方法来克服问题的不适定性是解决反问题的关键所在。对热传导正问题而言，具有较完整的理论体系及完善的算法过程，但对于热传导反问题而言因其具有不适定性，在本项目中，主要目的是进一步探索寻找稳定有效的数值方法求解原热传导反问题的近似解，对反问题中含若干个参数项，同时反求函数、热源等多参数辨识问题的数值逼近研究，此问题在理论分析、数值计算与应用等诸多工作上都需要做进一步的探讨。

Inverse Heat Conduction Problems (called IHCPs) have a wide range of applications in modern science, technology and engineering fields, such as heat fluid, the remote sensing technology, signal processing, continuum mechanics and industrial controlling etc., which have abstracted many researchers to study in the work. Since the external measured data is contaminated by noise errors, in the sense of Hadamard, IHCP is ill-posed, that is, any small disturbance in the data can result in an enormous change of numerical solution. Thus it can not keep the stability of solution. In order to overcome the ill-posedness of problem, it is key to find a stable numerical method for solving inverse problem. For the heat conduction direct problem, it has a more complete theoretical system and perfect algorithmic process, but for the inverse heat conduction problem, because of its ill-posedness, in this project, the main purpose is to further explore the search for stable and effective numerical methods to solve the approximate solution of the IHCP, the numerical approximation of the multi-parameter identification problem are presented and further to study in our work, including several parameter items, inverse functions and heat sources etc, this problem needs to be further explored in many aspects such as theoretical analysis, numerical calculation and application.