论文标题
非线性Stefan问题，用于一阶段通用热方程，并具有热通量和对流边界条件
Nonlinear Stefan Problem for one-phase generalized heat equation with heat flux and convective boundary condition
论文作者
论文摘要
在本文中，我们考虑了一个数学模型的闭合电气接触阶段的数学模型，该模型涉及金属蒸发，在固定面部瞬间爆炸瞬间爆炸爆炸，因为在固定面上爆炸了弧线点火$ p_0 $ $ p_0 $ $ z = 0 $，并在温度范围的范围内与轴向的范围$ neformircribre相比，与可变的横截面相比，与轴向的偏差相比，在材料中进行热传递，并忽略了轴向的范围，并且可以忽略均可予以量的范围。 =α（t）$。这种材料的液体区域中的温度场可以通过Stefan问题来建模，用于广义热方程。解决方案方法基于相似性变量，这使我们能够将广义热方程式减少到非线性普通微分方程。此外，我们必须确定液相的温度溶液和熔化界面的位置。通过使用固定点Banach定理证明了解决方案的存在和独特性。两种热系数的溶液，尤其是表示恒定和线性导热率，证明了每种溶液的存在和唯一性。
In this article we consider a mathematical model of an initial stage of closure electrical contact that involves a metallic vaporization after instantaneous exploding of contact due to arc ignition with power $P_0$ on fixed face $z=0$ and heat transfer in material with a variable cross section, when the radial component of the temperature gradient can be neglected in comparison with the axial component with heat flux and convective boundary conditions prescribed at the known free boundary $z = α(t)$. The temperature field in the liquid region of such kind of material can be modelled by Stefan problem for the generalized heat equation. The method of solution is based on similarity variable, which enables us to reduce generalized heat equation to nonlinear ordinary differential equation. Moreover, we have to determine temperature solution for the liquid phase and location of melting interface. Existence and uniqueness of the solution is proved by using the fixed point Banach theorem. The solution for two cases of thermal coefficients, in particular, constant and linear thermal conductivity are represented, existence and uniqueness for each type of solution is proved.
