Regularization within two-parameters for identification heat-coefficient in the parabolic equation

In this work, a new and promising method based on the minimization of a special functional that depends on two regularization parameters is considered for identification of the heat conduction coefficient in the parabolic equation. This method uses the adjoint and sensibility equations. One of the regularization parameters is associated with the heat-coefficient (as in conventional Tikhonov algorithms), but the other is associated with the derivative of the calculated solution. This work is the numerical complementation of the initial theoretical work of Doris Hinestroza Gutierrez, R.I.P. [5]. In this work, we use MATLAB minimization tools, using the finite element method in solving the direct problem, and numerical differentiation by two-sided difference quotient (see [12]) to show numerical examples; we perform a special example with a coefficient defined in pieces. Numerical comparisons of the proposed method with other reported methods will be analyzed. The bibliography has been updated, and some details of the initial writing have been corrected.