Abstract: We considered an inverse problem of simultaneous identification of the initial field and boundary heat flux for one-dimensional heat equation with Neumann boundary conditions. Firstly, the heat flux density and temperature at the right boundary and the terminal temperature were given, a model of Fredholm integral equation was established and the uniqueness of its solution was proved. Secondly, a regularization method for  simultaneous inversion of the heat flux density at the left boundary and initial temperature field was constructed. The results of numerical examples show that the data preprocessing algorithm and improved regularization method achieve higher accuracy of double-function inversion.

Key words: inverse problem, heat conduction equation, Neumann boundary condition, integral equation, regularization method