一类新型二相Stefan问题的研究

On a New Type of Two-Phase Stefan Problem

研究了一类新型二相Stefan问题,该问题在自由边界上的条件和一般的Stefan问题有较大的不同.在证明解的存在唯一性过程中,先将问题转化为等价的积分方程组,由此定义一Banach空间及其上的一个映照T.证明了T在该空间一闭子集上是压缩的,得到了积分方程组局部解的存在唯一性.由等价性也就证明了新型二相Stefan问题局部解的存在唯一性.用延拓方法得到了整体解的存在唯一性.最后讨论了解的适定性.

This paper is about a new type of two-phase Stefan problem.The Stefan problem is different from common Stefan problems on the free boundary.In order to attain the existence and uniqueness,first the Stefan problem into an equivalent system of integral equations was translated.Then a Banach space and a mapping T on it was defined.By proving that T is a contraction mapping on a closed subset of the Banach space,the existence and uniqueness of local solutions to the integral equations was gained.Because of the equivalence of the integral equations with Stefan problem,the existence and uniqueness of local solutions to the new type of Stefan problem was got,then apply the continuation method to get the existence and uniqueness of global solutions.Finally,discusses the well-possed of solutions.