论文标题
有限的时间自相似破裂在广义的弹性流体动力润滑模型中
Finite-time self-similar rupture in a generalized elastohydrodynamic lubrication model
论文作者
论文摘要
薄膜破裂是一种非线性不稳定性，可在有限的时间导致溶液降至零。我们研究了广义弹性流体动力润滑模型的有限时间破裂行为。该模型具有破坏压力的稳定与稳定弹性弯曲压力和表面张力之间的相互作用。理事方程是分别由迁移率函数中的指数和分离压力的指数参数化的六阶非线性抛物性部分微分方程。分析了由第六阶前阶方程控制的渐近自相似有限时间破裂溶液。在弱弹性极限中，还确定了由四阶相似性方程控制的瞬态自相似动力学。
Thin film rupture is a type of nonlinear instability that causes the solution to touch down to zero at finite time. We investigate the finite-time rupture behavior of a generalized elastohydrodynamic lubrication model. This model features the interplay between destabilizing disjoining pressure and stabilizing elastic bending pressure and surface tension. The governing equation is a sixth-order nonlinear degenerate parabolic partial differential equation parameterized by exponents in the mobility function and the disjoining pressure, respectively. Asymptotic self-similar finite-time rupture solutions governed by a sixth-order leading-order equation are analyzed. In the weak elasticity limit, transient self-similar dynamics governed by a fourth-order similarity equation are also identified.
