The heat flux identification problem for a nonlinear parabolic equation in 2D

We consider the heat flux identification problem (HFIP) based on the boundary measurements for a nonlinear parabolic equation in 2-dimensional space. The standard linearization algorithm is applied to the nonlinear direct problem. The method of Conjugate Gradient Algorithm, based on the gradient formula for the cost functional, is then proposed for numerical solution of the inverse heat flux problem. Numerical analysis of the algorithm applied to the inverse problem in typical classes of flux functions is presented. Computational results, obtained for random noisy output data, indicate how the iteration number of the Conjugate Gradient Algorithm can be estimated. Numerical results illustrate bounds of applicability of proposed algorithm, as well as its efficiency and accuracy.