  We first give a complete linearized stability analysis around stationary
solutions of the Mullins-Sekerka flow with $90^\circ$ contact angle in two
space dimensions. The stationary solutions include flat interfaces, as well as
arcs of circles. We investigate the different stability behaviour in dependence
of properties of the stationary solution, such as its curvature and length, as
well as the curvature of the boundary of the domain at the two contact points.
We show that the behaviour changes in terms of these parameters, ranging from
exponential stability to instability. We also give a first result on nonlinear
stability for curved boundaries.
