Weak solutions to lubrication equations in the presence of strong slippage
نویسندگان
چکیده
The existence of global weak solutions is proved for one-dimensional lubrication models that describe the dewetting process of nanoscopic thin polymer films on hydrophobyzed substrates and take account of large slippage at the polymer-substrate interface. The convergence of these solutions as either the Reynolds number or the capillarity goes to zero, as well as their limiting behaviour as the slip length goes to zero or infinity are investigated.
منابع مشابه
رفتار سالیتونی در مدلهای ناپایدار باروکیلینیک
Here we concern ouraelves with the derivation of a system of evolution equations for slowly varying amplitude of a baroclinic wave packet. The self-induced transparency, Sine-Gordon, and nonlinear Schrodinger equations, all of which possess soliton solutions, each arise for different inviscid limits. The presence of viscosity, however, alters the form of the evolution equations and changes th...
متن کاملFinite-time Blow-up of Solutions of Some Long-wave Unstable Thin Film Equations
We consider the family of long-wave unstable lubrication equations ht = −(hhxxx)x − (hhx)x with m ≥ 3. Given a fixed m ≥ 3, we prove the existence of a weak solution that becomes singular in finite time. Specifically, given compactly supported nonnegative initial data with negative energy, there is a time T∗ < ∞, determined by m and the H1 norm of the initial data, and a compactly supported non...
متن کاملExistence and uniqueness of weak solutions for a class of nonlinear divergence type diffusion equations
In this paper, we study the Neumann boundary value problem of a class of nonlinear divergence type diffusion equations. By a priori estimates, difference and variation techniques, we establish the existence and uniqueness of weak solutions of this problem.
متن کاملModeling of the beam discontinuity with two analyses in strong and weak forms using a torsional spring model
In this paper, a discontinuity in beams whose intensity is adjusted by the spring stiffness factor is modeled using a torsional spring. Adapting two analyses in strong and weak forms for discontinuous beams, the improved governing differential equations and the modified stiffness matrix are derived respectively. In the strong form, two different solution methods have been presented to make an a...
متن کاملModifying a Conventional Grasping Control Approach for Undesired Slippage Control in Cooperating Manipulator Systems
There have been many researches on object grasping in cooperating systems assuming no object slippage and stable grasp and the control system is designed to keep the contact force inside the friction cone to prevent the slippage. However undesired slippage can occur due to environmental conditions and many other reasons. In this research, dynamic analysis and control synthesis of a cooperating ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010