Sharp fronts in attracting-adatom monolayers

The problem of pattern formation by adsorbates undergoing attractive lateral interactions, is described by a parabolic integrodifferential equation having the scaled inverse temperature ϵ and the scaled pressure α of the vapor phase as parameters. A coexistence region of high- and low-coverage stable homogeneous states has been reported in the (ϵ, α) plane. In the small interaction-range limit an effective diffusion coefficient can be defined, which becomes however negative for a coverage range in between the stable homogeneous ones. A novel free-energy-like Lyapunov functional is found here for this problem. When evaluated on the homogeneous states, it leads to a Maxwell-like construction which selects essentially the same value α(ϵ) as the originally posited zero front-velocity condition. Moreover, its value on static fronts at this particular α(ϵ) coincides with those of the homogeneous states. This article is dedicated to Prof. Helmut Brand with occasion of his 60th birthday