Dipoles and similarity solutions of the thin film equation in the half-line
Dipoles and similarity solutions of the thin film equation in the half-line
复制标题
半直线薄膜方程的偶极子和相似解
DOI：
10.1088/0951-7715/13/2/305
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发表时间：
2000
期刊：
影响因子：
1.7
通讯作者：
J. King
中科院分区：
文献类型：
--
作者：
Francisco Bernis;J. Hulshof;J. King
我们考虑了薄膜方程ht +(hn hxxx)x = 0半线上的非负解，这出现在粘性薄膜、扩散液滴和Hele-Shaw细胞的润滑模型中。当x = 0是流体可以流出的边缘时，我们根据形式和建模参数讨论了x = 0处的边界条件。我们应用这一讨论定义了第一类和第二类相似解。根据边界条件，我们引入了第一类质量保持解（0<n <3），第二类“反常偶极子”（0<n <2, n 1）和第一类标准偶极子解（n = 1）。对于第一类解，我们证明了在x = 0处和在自由边界处的存在性、唯一性和渐近性。对于第二类解，我们简要地给出了一些定性性质。
We consider non-negative solutions on the half-line of the thin film equation ht +(hn hxxx )x = 0, which arises in lubrication models for thin viscous films, spreading droplets and Hele-Shaw cells. We present a discussion of the boundary conditions at x = 0 on the basis of formal and modelling arguments when x = 0 is an edge over which fluid can drain. We apply this discussion to define some similarity solutions of the first and the second kind. Depending on the boundary conditions, we introduce mass-preserving solutions of the first kind (0<n <3), `anomalous dipoles' of the second kind (0<n <2, n 1) and a standard dipole solution of the first kind for n = 1. For solutions of the first kind we prove results on existence, uniqueness and asymptotic behaviour, both at x = 0 and at the free boundary. For solutions of the second kind we briefly present some qualitative properties.
影响因子：
1.7
作者：
Brenner, MP;Constantin, P;Venkataramani, SC
通讯作者：
Venkataramani, SC