The free boundary of thin viscous flows
The free boundary of thin viscous flows
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稀薄粘性流的自由边界
DOI：
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发表时间：
1996
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影响因子：
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通讯作者：
Francisco Bernis
中科院分区：
文献类型：
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作者：
Francisco Bernis
我们考虑了四阶非线性退化抛物型方程Ut+(Un U Xxx)x=0，它出现在粘性薄膜和扩散液滴的润滑模型中，以及Hele-Shaw槽中细颈流体的流动中。二元合金的相分离理论(具有简并迁移率的Cahn-Hilliard方程)、某些塑性模型和生物系统的空间花纹形成研究中都存在类似简并性和/或附加低阶项的四阶抛物型方程。这位作者最近证明了，如果0 0且u=0。此外，当1/2<；n<；2时界面是Holder连续的，当0<；n≤1/2时界面是右连续的。最后，我们考虑了柯西问题，并给出了关于解的最优渐近速度的最新结果，以及当0<；n<；2；这些速度与源型(基本)解的最优渐近速度完全匹配时的t→∞。
We consider the fourth order nonlinear degenerate parabolic equation U t + (u n u xxx ) x = 0 which arises in lubrication models for thin viscous films and spreading droplets as well as in the flow of a thin neck of fluid in a Hele-Shaw cell. Fourth order parabolic equations with a similar type of degeneracy and/or additional lower order terms arise in the theory of phase separation for binary alloys (Cahn-Hilliard equation with degenerate mobility), in some plasticity models and in the study of spatial pattern formation in biological systems. This author has recently proved that if 0 0 and u = 0. Furthermore, the interface is Holder continuous if 1/2 < n < 2 and right-continuous if 0 < n ≤ 1/2. Finally we consider the Cauchy problem and present the recent results on optimal asymptotic rates as t → ∞ for the solution and for the interface when 0 < n < 2; these rates exactly match those of the source-type (fundamental) solutions.