- journal articles metadata
European Mathematical Society Publishing House
2024-03-28 14:15:28
4
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=IFB&vol=1&iss=2&update_since=2024-03-28
Interfaces and Free Boundaries
Interfaces Free Bound.
IFB
1463-9963
1463-9971
Partial differential equations
Numerical analysis
Fluid mechanics
Biology and other natural sciences
10.4171/IFB
http://www.ems-ph.org/doi/10.4171/IFB
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
1
1999
2
On the justification of the quasistationary approximation in the problem of motion of a viscous capillary drop
Vsevolod
Solonnikov
Russian Acadademy of Sciences, ST. PETERSBURG, RUSSIAN FEDERATION
Quasistationary approximation, viscous capillary drop
We prove that the free boundary problem governing the motion of an isolated liquid mass in the case of a small Reynolds number [egr] has a unique solution in a certain time interval (0, T0) independent of [egr] and we show that the difference of the solution and of the quasistationary approximation to the solution has order 0([egr]) for t [isin] (t0, T0) with arbitrary positive t0.
Functional analysis
Probability theory and stochastic processes
125
173
10.4171/IFB/7
http://www.ems-ph.org/doi/10.4171/IFB/7
Anisotropy in multi-phase systems: a phase field approach
Harald
Garcke
Universität Regensburg, REGENSBURG, GERMANY
Barbara
Stoth
Universität Bonn, BONN, GERMANY
B.
Nestler
RWTH Aachen, AACHEN, GERMANY
interface motion, multi-phase systems, anisotropic interfacial energy
A phase field concept for interface motion in general multi-phase systems with anisotropic interfacial energy is studied. We allow the anisotropy to be even crystalline which leads to a polygonial Wulff shape. A sharp interface model which appears as the limit of small interfacial thickness is stated. Through a series of numerical simulations we demonstrate that our concept can recover features like crystalline curvature flow, an anisotropic version of Young's law at triple-junctions and an anisotropic modification of the right angle condition at points where the interface intersects an external boundary. An important advantage of our approach is that there is a simple relation between the coefficients in the phase field model and the defining parameters of the sharp interface model.
Functional analysis
Probability theory and stochastic processes
175
198
10.4171/IFB/8
http://www.ems-ph.org/doi/10.4171/IFB/8
Existence for an Allen-Cahn/Cahn-Hilliard system with degenerate mobility
Roberta
Dal Passo
Università di Roma, ROMA, ITALY
Lorenzo
Giacomelli
Università di Roma La Sapienza, ROMA, ITALY
Amy
Novick-Cohen
Technion - Israel Institute of Technology, HAIFA, ISRAEL
Neumann problem, degenerate parabolic systems, phase separation, binary alloys
We prove existence in one space dimension of weak solutions for the Neumann problem for a degenerate parabolic system consisting of a fourth-order and a second-order equation with singular lower-order terms. This system arises in the description of phase separation and ordering in binary alloys.
Functional analysis
Probability theory and stochastic processes
199
226
10.4171/IFB/9
http://www.ems-ph.org/doi/10.4171/IFB/9
Error estimates for semi-discrete dendritic growth
Andreas
Veeser
Universität Freiburg, FREIBURG I BR, GERMANY
Stefan problem, dendritic growth
Semi-discrete approximations to a mathematical model for two-dimensional dendritic growth are analysed. The model is a Stefan problem with interfacial structure. The semi-discrete problem uses a parametrization for the free boundary and finite elements in space. The main results are a priori error estimates for the temperature field and the parametrization of the free boundary. The optimality of their order is discussed. Further error estimates concern approximations to relevant geometric (e.g. curvature) and measuring quantities.
Functional analysis
Probability theory and stochastic processes
227
255
10.4171/IFB/10
http://www.ems-ph.org/doi/10.4171/IFB/10