热流传播速度的数学分析

The Mathematical Analysis for the Propagation of Heat Flow

考虑满足Cattaneo-Vernotte定律的热传导,其热流传播速度是有限的,其温度分布函数满足一个双曲型方程。如果热传导满足Fourier实验定律,则热流传播速度是无穷大,这时温度分布函数满足热传导方程。本文在一维情形下证明当热流速度从有限趋于无限时,其对应的温度分布函数的一致收敛性,以及在多维情形下的L2强收敛性。

Considered in this paper is a heat flow which satisfys the Cattaneo-Vernotte Law, the propagation velocity of heat flow is finite, and its temperature distribution satisfies a hyperbolic equation. If the propagation of heat flow obeys Fourier law, then the propagation velocity of heat flow is infinite, in this case its temperature distribution satisfies a parabolic equation. In one dimensional case it is proved that the solutions of hyperbolic equations converge uniformly to the solution of parabolic equation when the propagation velocity of heat flow goes to infinity.