scholarly journals On self-similar solutions to the surface diffusion flow equations with contact angle boundary conditions

2014 ◽  
Vol 16 (4) ◽  
pp. 539-573 ◽  
Author(s):  
Tomoro Asai ◽  
Yoshikazu Giga
Keyword(s):  
Contact Angle ◽  
Boundary Conditions ◽  
Surface Diffusion ◽  
Diffusion Flow ◽  
Flow Equations ◽  
Surface Diffusion Flow ◽  
Self Similar ◽  
Similar Solutions

scholarly journals The self-similar solution for draining in the thin film equation

2004 ◽  
Vol 15 (3) ◽  
pp. 329-346 ◽  
Author(s):  
JAN BOUWE VAN DEN BERG ◽  
MARK BOWEN ◽  
JOHN R. KING ◽  
M. M. A. EL-SHEIKH
Keyword(s):  
Thin Film ◽  
Contact Angle ◽  
Boundary Conditions ◽  
Finite Domain ◽  
Series Solutions ◽  
Self Similar Solution ◽  
Power Series Solutions ◽  
Thin Film Equation ◽  
Self Similar ◽  
Similar Solutions

We investigate self-similar solutions of the thin film equation in the case of zero contact angle boundary conditions on a finite domain. We prove existence and uniqueness of such a solution and determine the asymptotic behaviour as the exponent in the equation approaches the critical value at which zero contact angle boundary conditions become untenable. Numerical and power-series solutions are also presented.

scholarly journals Global existence and stability for the modified Mullins–Sekerka and surface diffusion flow

2022 ◽  
Vol 4 (6) ◽  
pp. 1-104
Author(s):  
Serena Della Corte ◽  
◽  
Antonia Diana ◽  
Carlo Mantegazza ◽  
◽  
...  
Keyword(s):  
Surface Diffusion ◽  
State Of The Art ◽  
Gradient Flow ◽  
Necessary And Sufficient Condition ◽  
Diffusion Flow ◽  
Critical Set ◽  
Surface Diffusion Flow ◽  
Area Functional ◽  
Existence And Stability ◽  
Necessary And Sufficient

<abstract><p>In this survey we present the state of the art about the asymptotic behavior and stability of the <italic>modified Mullins</italic>–<italic>Sekerka flow</italic> and the <italic>surface diffusion flow</italic> of smooth sets, mainly due to E. Acerbi, N. Fusco, V. Julin and M. Morini. First we discuss in detail the properties of the nonlocal Area functional under a volume constraint, of which the two flows are the gradient flow with respect to suitable norms, in particular, we define the <italic>strict stability</italic> property for a critical set of such functional and we show that it is a necessary and sufficient condition for minimality under $ W^{2, p} $–perturbations, holding in any dimension. Then, we show that, in dimensions two and three, for initial sets sufficiently "close" to a smooth <italic>strictly stable critical</italic> set $ E $, both flows exist for all positive times and asymptotically "converge" to a translate of $ E $.</p></abstract>

scholarly journals The Surface Diffusion Flow with Elasticity in Three Dimensions

2020 ◽  
Vol 237 (3) ◽  
pp. 1325-1382
Author(s):  
Nicola Fusco ◽  
Vesa Julin ◽  
Massimiliano Morini
Keyword(s):  
Surface Diffusion ◽  
Three Dimensions ◽  
Diffusion Flow ◽  
Surface Diffusion Flow

scholarly journals The Surface Diffusion Flow for Immersed Hypersurfaces

1998 ◽  
Vol 29 (6) ◽  
pp. 1419-1433 ◽  
Author(s):  
Joachim Escher ◽  
Uwe F. Mayer ◽  
Gieri Simonett
Keyword(s):  
Surface Diffusion ◽  
Diffusion Flow ◽  
Surface Diffusion Flow
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