Spherically symmetric Stefan problem with the Gibbs–Thomson law at the moving boundary
Spherically symmetric Stefan problem with the Gibbs–Thomson law at the moving boundary
复制标题
移动边界处具有吉布斯-汤姆逊定律的球对称 Stefan 问题
DOI：
10.1017/s0956792500002345
复制
发表时间：
1996
影响因子：
1.9
通讯作者：
M. Primicerio
中科院分区：
文献类型：
--
作者：
I. Götz;M. Primicerio
本文研究三维空间中球对称Stefan问题。熔化温度满足吉布斯-汤姆逊定律。该解决方案是作为一个限制的解决方案，类似的问题，包含一个小的额外的动力学项的熔化温度。在一些结构假设下，我们证明相变边界最多有一个不连续点t = T0（参见Götz & Zaltzman（1995）中平面Stefan问题的相应结果）。在单相问题中，间断点总是存在的。在时间T0，整个固相瞬间熔化。我们还研究了满足恒温器型边界条件的定常解的渐近稳定性（t → ∞）。
This paper deals with the spherically symmetric Stefan problem in three space dimensions. The melting temperature satisfies the Gibbs–Thomson law. The solution is obtained as a limit of solutions of similar problems containing a small additional kinetic term in the melting temperature. Under some structural assumptions we show that the phase-change boundary has at most one discontinuity point t = T0 (see the corresponding result for the planar Stefan problem in Götz & Zaltzman (1995)). In the one-phase problem the discontinuity point always exists. At the time T0 the whole solid phase melts instantaneously. We study also the asymptotical stability (t → ∞) of stationary solutions satisfying boundary conditions of thermostat type.