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

M. A. Davydova   ; G. D. Rublev

Teoretičeskaâ i matematičeskaâ fizika, Tome 220 (2024) no. 2, pp. 237-260

Résumé

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.

Détail

Keywords: stationary thermal structures, nonlinear heat conductance problems, asymptotic methods, solutions with internal transition layers, inverse coefficient problems, methods for reconstructing thermophysical characteristics of nonlinear media, determination of the thermal conductivity coefficient.

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