Mass conserved Allen-Cahn equation and volume preserving mean curvature flow

Xinfu Chen, Danielle Hilhorst, Elisabeth Logak

We consider a mass conserved Allen-Cahn equation $u_t=Δu+ \e^{-2} (f(u)-\eλ(t))$ in a bounded domain with no flux boundary condition, where $\eλ(t)$ is the average of $f(u(\cdot,t)…