  We investigate the formation and the coarsening dynamics of islands in a
strained epitaxial semi-conductor film. These islands are commonly observed in
thin films undergoing a morphological instability due to the presence of the
elasto capillary effect. We first describe both analytically and numerically
the formation of an equilibrium island using a two dimensional continuous
model. We have found that these equilibrium island-like solutions have a
maximum height $h_0$ and they sit on top of a flat wetting layer with a
thickness $h_w$. We then consider two islands and we report that they undergo a
non-interrupted coarsening that follows a two stage dynamics. The first stage
may be depicted by a quasi-static dynamics, where the mass transfers are
proportional to the chemical potential difference of the islands. It is
associated with a time scale $t_c$ that is function of the distance $d$ between
the islands, and leads to the shrinkage of the smallest island. Once its height
becomes smaller than a minimal equilibrium height $h_{0}^{*}$, its mass spreads
over the entire system. Our results pave the way for a future analysis of
coarsening of an assembly of islands.
