一个多维油漆干燥过程的自由边界问题

A Free-boundary Problem of Multi-dimensional Paint Drying Process

油漆干燥问题在数学上表现为一个相变过程,其模型是著名的Stefan问题,但该模型与普通的相变问题自由边界条件不同。如果把墙面近似看作一点,只考虑油漆厚度,则模型表现为一维的,已有学者证明了一维问题解的存在性。对多维情形还没有结果。文章研究了油漆干燥过程的多维模型,并利用拉直边界、不动点技术和抛物型方程弱解的Holder连续性技巧证明了这个问题整体连续解的存在唯一性。

The process of paint drying is mathematically expressed as a phase transition whose model is a fa- mous Stefan problem. But the condition of free - boundary of our model is dissimilar with that of ordinary phase transition problem. If the wall was approximately considered as a point and only paint thickness was taken into con- sideration, the model was a one - dimensional one and the existence of solution had been obtained. There has no solution to the multi- dimensional situation. In this study, the multi -dimensional model for paint drying process was analyzed. And the existence, uniqueness of the global continuous solutions to the problem were given by meth- od of straightening boundary, fixed point technique and skill of Holder＇ s continuity of weak solution to parabolic type？ equation.