Mass conserved Allen-Cahn equation and volume preserving mean curvature flow
نویسنده
چکیده
We consider a mass conserved Allen-Cahn equation ut = ∆u + 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 approaches, as ε ց 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.
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