Multidimensional thermal structures in the singularly perturbed stationary models of heat and mass transfer with a nonlinear thermal diffusion coefficient
Multidimensional thermal structures in the singularly perturbed stationary models of heat and mass transfer with a nonlinear thermal diffusion coefficient
Zakharova, S. A. 1Davydova, M. A.1
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作者信息
1. Moscow MV Lomonosov State Univ
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Abstract
A new approach to the study of multidimensional singularly perturbed problems of nonlinear heat conduction is proposed, based on the further development and use of asymptotic analysis methods. We study the question of the existence of classical Lyapunov stable stationary solutions with boundary and internal transition layers (stationary thermal structures) of the nonlinear heat transfer equation. We suggest the efficient algorithm for constructing an asymptotic approximation to the localization surface of the transition layer. To justify the constructed formal asymptotics, we use the principle of comparison. We consider the application of the results of asymptotic analysis to solving inverse problem of reconstructing the temperature dependence of the thermal conductivity coefficient from a known position of the internal layer of thermal structure. (C) 2021 Elsevier B.V. All rights reserved.
Key words
Nonlinear heat conductivity/Reaction-diffusion-advection equations/Contrast structures/Thermal structures in the nonlinear dissipative media/Asymptotic methods/Inverse coefficient problems/EXISTENCE/BOUNDARY/LAYERS
NSTL
Elsevier