The thin-film equation close to self-similarity
The thin-film equation close to self-similarity
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接近自相似性的薄膜方程
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Christian Seis
中科院分区：
文献类型：
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作者：
Christian Seis
在本工作中，我们研究了具有线性迁移率的多维薄膜方程在自相似Smyth-Hill解附近的适定性和正则性。更具体地说，我们执行冯米塞斯变化的独立和独立的变量，将薄膜自由边界问题转化为单位球上的抛物方程。我们表明，转换后的方程是适定的，解决方案是光滑的，甚至在时间和角度方向上的分析。后者需要解析的水平集的原始方程，因此，特别是自由边界。
In the present work, we study well-posedness and regularity of the multidimensional thin film equation with linear mobility in a neighborhood of the self-similar Smyth--Hill solutions. To be more specific, we perform a von Mises change of dependent and independent variables that transforms the thin film free boundary problem into a parabolic equation on the unit ball. We show that the transformed equation is well-posed and that solutions are smooth and even analytic in time and angular direction. The latter entails the analyticity of level sets of the original equation, and thus, in particular, of the free boundary.