Buffer phenomenon in the spatially one-dimensional Swift–Hohenberg equation

We consider a boundary value problem for the spatially one-dimensional Swift–Hohenberg equation with zero Neumann boundary conditions at the endpoints of a finite interval. We establish that as the length $l$ of the interval increases while the supercriticality $\varepsilon$ is fixed and sufficiently small, the number of coexisting stable equilibrium states in this problem indefinitely increases; i.e., the well-known buffer phenomenon is observed. A similar result is obtained in the $2l$-periodic case.