Geodesic
Mass conserving Allen–Cahn equation and volume preserving mean curvature flow
Xinfu Chen1 ; Danielle Hilhorst2 ; Elisabeth Logak3
1University of Pittsburgh, United States
2Université Paris-Sud, Orsay, France
3Université de Cergy-Pontoise, France
Interfaces and free boundaries, Tome 12 (2010) no. 4, pp. 527-549

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DOI

We consider a mass conserving Allen–Cahn equation ut​=Δu+ε–2(f(u)–ελ(t)) in a bounded domain with no flux boundary condition, where ελ(t) is the average of f(u(⋅,t)) and –f is the derivative of a double equal well potential. Given a smooth hypersurface γ0​ contained in the domain, we show that the solution uε with appropriate initial data tends, as ε↘0, to a limit which takes only two values, with the jump occurring at the hypersurface obtained from the volume preserving mean curvature flow starting from γ0​.
DOI : 10.4171/ifb/244
Classification : 00-XX

Xinfu Chen  1   ; Danielle Hilhorst  2   ; Elisabeth Logak  3

1 University of Pittsburgh, United States
2 Université Paris-Sud, Orsay, France
3 Université de Cergy-Pontoise, France 
Xinfu Chen; Danielle Hilhorst; Elisabeth Logak. Mass conserving Allen–Cahn equation and volume preserving mean curvature flow. Interfaces and free boundaries, Tome 12 (2010) no. 4, pp. 527-549. doi: 10.4171/ifb/244
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     title = {Mass conserving {Allen{\textendash}Cahn} equation and volume preserving mean curvature flow},
     journal = {Interfaces and free boundaries},
     pages = {527--549},
     year = {2010},
     volume = {12},
     number = {4},
     doi = {10.4171/ifb/244},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/244/}
}
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