  Phase field crystal is a model used to describe the behavior of crystalline
materials at the mesoscale. In this study, we investigate the well-posedness of
a phase field crystal equation subject to a degenerate mobility $M(u)$ that
equals zero for $u\leq 0$. First, we prove the existence of a weak solution to
a phase field crystal equation with non-degenerate cutoff mobility. Then,
assuming that the initial data $u_0(x)$ is positive, we establish the existence
of a nonnegative weak solution to the degenerate case. Such solution is the
limit of solutions corresponding to non-degenerate mobilities. We also verify
that such a weak solution satisfies an energy dissipation inequality.
