Identification of the thermal conductivity coefficient in the three-dimensional case by solving a corresponding optimization problem

The inverse problem of determining a temperature-dependent thermal conductivity coefficient in a parallelepiped is considered and investigated. The consideration is based on the Dirichlet boundary value problem for the three-dimensional nonstationary heat equation. The coefficient inverse problem is reduced to an optimization problem, which is solved numerically by applying gradient methods for functional minimization. The performance and efficiency of the proposed approach are demonstrated by solving several nonlinear problems with temperature-dependent coefficients.