Exponential Asymptotics for Thin Film Rupture
Exponential Asymptotics for Thin Film Rupture
复制标题
薄膜破裂的指数渐进
DOI：
--
复制
发表时间：
2013
影响因子：
1.9
通讯作者：
Thomas P. Witelski
中科院分区：
文献类型：
--
作者：
S. Chapman;Philippe H. Trinh;Thomas P. Witelski
许多物理系统模型中奇点的形成可以用自相似解来描述。一个特别的例子是涂在固体基底上的粘性流体薄膜的有限时间破裂。以往的研究表明，存在一个离散的，可数无穷多个不同的解的非线性微分方程描述的自相似行为。然而，没有确定这些解决方案的分析机制。在本文中，我们使用指数渐近的技术来构造的相似解的无穷序列的分析选择条件，确认早期的数值研究的成果。
The formation of singularities in models of many physical systems can be described using self-similar solutions. One particular example is the finite-time rupture of a thin film of viscous fluid which coats a solid substrate. Previous studies have suggested the existence of a discrete, countably infinite number of distinct solutions of the nonlinear differential equation which describes the self-similar behavior. However, no analytical mechanism for determining these solutions was identified. In this paper, we use techniques in exponential asymptotics to construct the analytical selection condition for the infinite sequence of similarity solutions, confirming the conjectures of earlier numerical studies.