一类描述冰融解的自由边界问题

The melting of ice described by the free boundary

考虑以具有双自由边界的抛物系统为模型的冰的融解问题,运用压缩映像原理和适当的估计证明了系统解的全局存在唯一性,并且通过对自由边界性态的研究可知,若0℃的冰内部有水存在,则无论水的初始温度如何,冰都将在某一时刻停止融解.

This paper deals with the problem about the mehing of ice in contact with water, which is described by a simple epidemic model with two free boundaries. The global existence and unique- ness of the solution to the system are proved by applying the contraction mapping theorem and some estimates. The result shows that if water is crowded by ice with 0 ℃, then no matter what is the initial temperature of water, the mehing of ice will stop at some time.