$$\frac{\partial\phi(\mathbf{x},t)}{\partial t}=\varepsilon^{2}\Delta\phi-F^{'}(\phi),\ \ \ \mathbf{x}\in \Omega,t>0$$ $$\frac{\partial \phi}{\partial\mathbf{n}}=0\ \ \text{on} \ \partial\Omega$$ $$\phi(\mathbf{x},0)=\phi_{0}(\mathbf{x}),\ \ \mathbf{x}\in \Omega$$
where $F(\phi)=0.25(\phi^2-1)^2$. In some literature, a conclusion says: after certain amount of time, three regions emerge: two phase regions where $\phi ≈ 1$ and −1, respectively, and an interfacial region which is very thin and connects the phase regions. Why? How to explain this interesting conclusion?