Numerical solution of the inverse coefficient problem for nonlinear heat conduction equation in orthotropic formulation (Q1285460)

Nonlinear heat equations with two space variables are often met in heat researches of anisotropic (orthotropic) materials. In a case with orthotropic materials there are two different nonlinear coefficients introducing the derivatives in relation to the two different space variables in the heat equation. The author considers an inverse heat problem connected with determining the nonlinear coefficients using an additional information about a solution of the heat boundary problem. A numerical minimization method and a gradient method are used to get the nonlinear coefficients of the inverse heat problem. The uniqueness of the solution is provided under some restrictions on the boundary conditions. It is noted that the numerical method of solving the inverse heat problem presented in the article can be used parallel with a method of regularized differentiation.