A complete recovery of the unknown

A complete recovery of the unknown temperature is attainable from solving a well-posed forward heat conduction problem if appropriate initial distribution and boundary conditions are given. However, in many practical applications, the boundary data can only be measured on a portion of the boundary or some points in the physical domain. This leads to the classical inverse heat conduction problems(IHCPs) that are highly ill-posed in the sense that their solutions do not continuously depend on the given known conditions[1]. The numerical situations get more severe when the observed data contain measurement error. Nonetheless, the IHCP is of high importance in many branches of engineering and science[2].