Determination of the Time-Dependent Thermal Conductivity in the Heat Equation with Spacewise Dependent Heat Capacity

摘要

In this paper, we consider an inverse problem of determining the time-dependent thermal conductivity from Cauchy data in a one-dimensional heat equation with space-dependent heat capacity. The parabolic partial differential equation is discretised using the finite -difference method and the inverse problem is recast as a nonlinear least-squares minimization. This is solved using the Isqnonlin routine from the MATLAB toolbox. Numerical results are presented and discussed showing that accurate and stable numerical solutions are achieved.