Identification of unknown parameters for heat conductivity equations

An algorithm for identification of unknown parameters of nonlinear heat conductivity equations is proposed. Solutions of equations observed with an error are input data of the algorithm. Finite dimensional approximations of input signals and their derivatives are used. The algorithm utilizes the idea of the direct minimization of the residual of equations written in an appropriate variational form. The convergence of the algorithm output to the set of all parameters compatible with the exact solution is proved. The paper is illustrated by computer simulations related to the identification of heat conductivity coefficients depending upon spatial variables and the temperature.