  This paper is concerned with establishing global asymptotic stability results
for a class of non-linear PDE which have some similarity to the PDE of the
Lifschitz-Slyozov-Wagner model. The method of proof does not involve a
Lyapounov function. It is shown that stability for the PDE is equivalent to
stability for a differential delay equation. Stability for the delay equation
is proven by exploiting certain maximal properties. These are established by
using the methods of optimal control theory.
