Geodesic
Convergence of a mass conserving Allen–Cahn equation whose Lagrange multiplier is nonlocal and local
Matthieu Alfaro1 ; Pierre Alifrangis1
1Université de Montpellier II, France
Interfaces and free boundaries, Tome 16 (2014) no. 2, pp. 243-268

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DOI

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.
DOI : 10.4171/ifb/319
Classification : 35-XX, 53-XX
Mots-clés : Mass conserving Allen–Cahn equation, singular perturbation, volume preserving mean curvature flow, matched asymptotic expansions, error estimates

Matthieu Alfaro  1   ; Pierre Alifrangis  1

1 Université de Montpellier II, France 
Matthieu Alfaro; Pierre Alifrangis. Convergence of a mass conserving Allen–Cahn equation whose Lagrange multiplier is nonlocal and local. Interfaces and free boundaries, Tome 16 (2014) no. 2, pp. 243-268. doi: 10.4171/ifb/319
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     author = {Matthieu Alfaro and Pierre Alifrangis},
     title = {Convergence of a mass conserving {Allen{\textendash}Cahn} equation whose {Lagrange} multiplier is nonlocal and local},
     journal = {Interfaces and free boundaries},
     pages = {243--268},
     year = {2014},
     volume = {16},
     number = {2},
     doi = {10.4171/ifb/319},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/319/}
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