Investigation of Well-Posedness of Solution for an IHCP

In this work, we consider an inverse heat conduction problem (IHCP). The given heat conduction equation and the initial-boundary conditions, are presented in a dimensionless form. By using a linear transformation, the ill-posed IHCP turns into a Cauchy problem. This problem is solved by the Legendre polynomials method. The existence, uniqueness and stability of the solution are proved.