Global dynamics of boundary droplets (Q379685)

In this paper, the authors consider the mass-conserving Allen-Cahn equation in a open bounded domain \(\Omega\subset \mathbb{R}^2\) with smooth boundary \(\partial \Omega\). They prove the existence of a global invariant manifold for the bubble states, which are states having a roughly semicircular interface attached to the boundary of the domain. Moreover, they describe the dynamics for the center of the bubble.