| Abstract: |
| We consider the mass-preserving $L^2$ -gradient flow of the weak or strong scaling of the functionalized Cahn-Hilliard equation and justify its sharp interface limit. With a suitable mass condition, the accumulated material forms a bilayer interface with width $\varepsilon$, which balances with the bulk phase. In the weak scaling case, we rigorously demonstrate that for well-prepared initial data, as the interface width $\varepsilon$ tends to zero, the bilayer interface converges to an area-preserving Willmore flow. This result holds for any dimension $n$ . |
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