中文摘要：

考虑了一个具有内部物质对流和非线性边界热交换的多维连铸Stefan问题,并得到了这个问题整体弱解的存在性、唯一性和对初边界条件的连续依赖性。本项工作改进和推广了J.F.Fodri-gues＆F.Yi的结果,放宽了他们对内部流和边界条件的一些不太符合实际的限制。

英文摘要：

A multiple dimensional continuous casting Stefan problem with internal convection of a material and nonlinear boundary heat exchange is considered. The existence, uniqueness and dependence to Initial boundary condition of globally weak solution of this problem are obtained. This work improves and extends the results of J. F. Rodri - gues ＆ F. Yi, relaxes restrictions that does not be to accord with reality very much on flux and boundary conditions in their articles.