Czochralski单晶拉制过程中一种自由边界问题整体解的存在唯一性

Existence and Uniqueness of Global Solutions of a Free Boundary Problem in the Process of Czochralski Crystal Growth

通过引入由晶体温度u(x,t)和晶体的自由边界s(t)构成的向量空间Sd,以及定义在其上的映射d,研究了基于Czochralski单晶拉制方法的数学模型中一类自由边界问题解的存在唯一性.采用压缩映照原理方法证明了该问题在Banach空间(Sd,d)上局部解的存在唯一性,并利用延拓方法得到了整体经典解的存在唯一性.

By introducing a metric space composed with the crystal temperature u（x,t） and free boundry s（t）,and defineing a mapping d on the space,we studied existence and uniqueness of solutions to a free boudury problem based on the process of czochralski crystal growth.Existence and uniqueness of local solutions is proved by contraction mapping principle on the banach space（Sd,d）,and the existence and uniqueness of global solutions is also obtained by applying the continuation method.