- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:04
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
16
2014
2
Convergence of a mass conserving Allen–Cahn equation whose Lagrange multiplier is nonlocal and local
Matthieu
Alfaro
Université de Montpellier II, MONTPELLIER CEDEX 5, FRANCE
Pierre
Alifrangis
Université de Montpellier II, MONTPELLIER CEDEX 5, FRANCE
Mass conserving Allen–Cahn equation, singular perturbation, volume preserving mean curvature flow, matched asymptotic expansions, error estimates
We consider the mass conserving Allen–Cahn equation proposed in [8]: the Lagrange multiplier which ensures the conservation of the mass contains not only nonlocal but also local effects (in contrast with [14]). As a parameter related to the thickness of a diffuse internal layer tends to zero, we perform formal asymptotic expansions of the solution. Then, equipped with this approximate solution, we rigorously prove the convergence to the volume preserving mean curvature flow, under the assumption that a classical solution of the latter exists. This requires a precise analysis of the error between the actual and the approximate Lagrange multipliers.
Partial differential equations
Differential geometry
243
268
10.4171/IFB/319
http://www.ems-ph.org/doi/10.4171/IFB/319