具温度边界条件的单相Stefan问题解的存在唯一性

摘要

证明了一种带有温度边界条件的Stefan问题解的存在唯一性.首先利用Green恒等式将问题转化为等价的积分方程组,由压缩映照原理得到了问题的局部解.再利用延拓方法得到了整体解.%Existence and uniqueness of global solutions for a one-phase Stefan problem are proved in this paper. The author firstly translates the Stefan problem into an equivalent system of integral equations with the help of Green Identity and has the existence and uniqueness of local solutions to the integral equations by contraction mapping theorem, then applies the continuation method to get the existence and uniqueness of global solutions.