Coefficient Inverse Problem for the Hyperbolic Equation of Thermal Conductivity in Two-Layer Soil

Understanding energy distribution across multiple layers is crucial in various engineering, ecological, and earth science disciplines. A particularly significant challenge is determining the thermophysical parameters of soil. This paper presents an inverse problem approach to identifying the thermal-conductivity characteristics of a two-layer soil using an analytical solution derived from a hyperbolic thermal conductivity equation.The study is based on experimental data obtained from two containers filled with distinct materials—one containing clay and the other black soil. First, the paper introduces an algorithm for solving the direct problem under first-kind boundary conditions within the experimental domain, utilizing the Fourier method. One of the main advantages of this analytical solution is that it provides an explicit, closed-form expression for the temperature distribution in each layer, in contrast to numerical methods.Subsequently, the thermal conductivity properties of the multilayer medium are determined numerically using the Gauss-Newton method, which is calibrated against experimentally measured temperature values at specific points in the region. The results validate both the solution to the direct problem and the accuracy of the coefficient identification process.