Global existence and stability for the modified Mullins–Sekerka and surface diffusion flow

<abstract><p>In this survey we present the state of art about asymptotic behavior and stability <italic>modified Mullins</italic>–<italic>Sekerka flow</italic> <italic>surface diffusion smooth sets, mainly due to E. Acerbi, N. Fusco, V. Julin M. Morini. First discuss in detail properties nonlocal Area functional under a volume constraint, which two flows are gradient flow with respect suitable norms, particular, define <italic>strict stability</italic> property for critical set such show that it is necessary sufficient condition minimality $ W^{2, p} $–perturbations, holding any dimension. Then, that, dimensions three, initial sets sufficiently "close" <italic>strictly stable critical</italic> E $, both exist all positive times asymptotically "converge" translate $.</p></abstract>