A stability theorem for diffusion problems with sharply changing temperature-dependent coefficients

In a previous work, a nonlinear heat conduction problem was considered, and the continuous dependence of its solution on the heat capacity and thermal conductivity of the medium was proved. However, considerable drawbacks arise in applying the results to some special practical cases. In order to provide a meaningful stability theorem for these special cases, a more sophisticated approach is used starting from a new weak formulation of the basic heat conduction problem.