Stationary thermal front in the problem of reconstructing the semiconductor thermal conductivity coefficient using simulation data

We study the problem of the existence of stationary, asymptotically Lyapunov-stable solutions with internal transition layers in nonlinear heat conductance problems with a thermal flow containing a negative exponent. We formulate sufficient conditions for the existence of classical solutions with internal layers in such problems. We construct an asymptotic approximation of an arbitrary-order for the solution with a transition layer. We substantiate the algorithm for constructing the formal asymptotics and study the asymptotic Lyapunov stability of the stationary solution with an internal layer as a solution of the corresponding parabolic problem with the description of the local attraction domain of the stable stationary solution. As an application, we present a new effective method for reconstructing the nonlinear thermal conductivity coefficient with a negative exponent using the position of the stationary thermal front in combination with observation data.