非Fourier温度场分布的奇摄动解
摘要
A temperature field model for single-layer materials was constructed with the non-Fourier heat conduction law, i.e. a type of singularly perturbed hyperbolic equations with small parameters in an unbounded domain. The asymptotic solution to the problem was obtained with the singularly perturbed expansion method. Firstly, the singular perturbation method was used to obtain the external solution and boundary layer correction terms of the problem. Through estimation of the maximum norms of the internal solution and the external solution, and the maximum norms of the time derivative, and under the theory of linear parabolic equations, the existence and uniqueness of the internal and external solutions were obtained, and the formal asymptotic expansion of the solution was obtained. The L<sup>2</sup> estimator of the asymptotic solution was given with the remainder estimator. The uniform validity of the asymptotic solution and the distribution of the temperature field in the unbounded domain were got. Through singular perturbation analysis, the relationship between the non-Fourier temperature field and the Fourier temperature field was given, and the specific behaviors of the non-Fourier temperature field were described.