scholarly journals Classical solvability of the multidimensional free boundary problem for the thin film equation with quadratic mobility in the case of partial wetting

2017 ◽  
Vol 37 (7) ◽  
pp. 3625-3699 ◽  
Author(s):  
Sergey Degtyarev
Keyword(s):  
Thin Film ◽  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Classical Solvability ◽  
Partial Wetting ◽  
Thin Film Equation

scholarly journals Thin-film models for an active gel

2018 ◽  
Vol 474 (2220) ◽  
pp. 20170828 ◽  
Author(s):  
G. Kitavtsev ◽  
A. Münch ◽  
B. Wagner
Keyword(s):  
Thin Film ◽  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Order Parameter ◽  
Active Liquid ◽  
Scalar Order Parameter ◽  
Significant Extension ◽  
The Rich ◽  
A Free Boundary Problem

In this study, we present a free-boundary problem for an active liquid crystal starting with the Beris–Edwards theory that uses a tensorial order parameter and includes active contributions to the stress tensor and then derive from it the Eriksen model for an active polar gel and scalar order parameter to analyse the rich defect structure observed in applications such as the adenosinetriphosphate-driven motion of a thin film of an actin filament network. The small aspect ratio of the film geometry allows for an asymptotic approximation of the free-boundary problem in the limit of weak elasticity of the network and strong active terms. The new thin-film model captures the defect dynamics in the bulk as well as wall defects and thus presents a significant extension of previous models based on the Leslie–Erickson–Parodi theory. As an example we derive the explicit solution for an active gel confined to a channel, which has discontinuous director profile leading to a bidirectional flow structure generated by the active terms.

The "Linear" Limit of Thin Film Flows as an Obstacle-Type Free Boundary Problem

2000 ◽  
Vol 61 (3) ◽  
pp. 1062-1079 ◽  
Author(s):  
Fernando Quirós ◽  
Francisco Bernis ◽  
Josephus Hulshof
Keyword(s):  
Thin Film ◽  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Linear Limit ◽  
Film Flows

On continuous branches of very singular similarity solutions of the stable thin film equation. II – Free-boundary problems

2011 ◽  
Vol 22 (3) ◽  
pp. 245-265 ◽  
Author(s):  
J. D. EVANS ◽  
V. A. GALAKTIONOV
Keyword(s):  
Thin Film ◽  
Cauchy Problem ◽  
Free Boundary ◽  
Boundary Problem ◽  
Similarity Solutions ◽  
Thin Film Equation ◽  
The Cauchy Problem ◽  
Self Similar ◽  
Image Position ◽  
Similar Solutions

We discuss the fourth-order thin film equation with a stable second-order diffusion term, in the context of a standard free-boundary problem with zero height, zero contact angle and zero-flux conditions imposed at an interface. For the first critical exponent where N ≥ 1 is the space dimension, there are continuous sets (branches) of source-type very singular self-similar solutions of the form For p ≠ p0, the set of very singular self-similar solutions is shown to be finite and consists of a countable family of branches (in the parameter p) of similarity profiles that originate at a sequence of critical exponents {pl, l ≥ 0}. At p = pl, these branches appear via a non-linear bifurcation mechanism from a countable set of second kind similarity solutions of the pure thin film equation Such solutions are detected by a combination of linear and non-linear ‘Hermitian spectral theory’, which allows the application of an analytical n-branching approach. In order to connect with the Cauchy problem in Part I, we identify the cauchy problem solutions as suitable ‘limits’ of the free-boundary problem solutions.

Uniqueness of solution to a free boundary problem from combustion with transport

MAT Serie A ◽  
2001 ◽  
Vol 5 ◽  
pp. 37-41
Author(s):  
Claudia Lederman ◽  
Juan Luis Vázquez ◽  
Noemí Wolanski
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Uniqueness Of Solution ◽  
A Free Boundary Problem

EXISTENCE OF PERIODIC SOLUTIONS FOR A FREE BOUNDARY PROBLEM OF HYPERBOLIC TYPE

2008 ◽  
Vol 05 (04) ◽  
pp. 785-806
Author(s):  
KAZUAKI NAKANE ◽  
TOMOKO SHINOHARA
Keyword(s):  
Mathematical Model ◽  
Free Boundary ◽  
Hyperbolic Equation ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Physical Phenomenon ◽  
Hyperbolic Type ◽  
Existence Of Periodic Solutions ◽  
A Free Boundary Problem ◽  
Thin Tape

A free boundary problem that arises from the physical phenomenon of "peeling a thin tape from a domain" is treated. In this phenomenon, the movement of the tape is governed by a hyperbolic equation and is affected by the peeling front. We are interested in the behavior of the peeling front, especially, the phenomenon of self-excitation vibration. In the present paper, a mathematical model of this phenomenon is proposed. The cause of this vibration is discussed in terms of adhesion.

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