  In this paper, we investigate the dynamics of solutions of the Muskat
equation with initial interface consisting of multiple corners allowing for
linear growth at infinity. Specifically, we prove that if the initial data
contains a finite set of small corners then we can find a precise description
of the solution showing how these corners desingularize and move at the same
time.
  At the analytical level, we are solving a small data critical problem which
requires renormalization. This is accomplished using a nonlinear change of
variables which serves as a logarithmic correction and accurately describes the
motion of the corners during the evolution.
