  In this paper we give an elementary proof of uniqueness of solutions to a
gas-disk interaction system with diffusive boundary condition. Existence of
near-equilibrium solutions for this type of systems with various boundary
conditions has been extensively studied in [1-8, 10]. However, the uniqueness
has been an open problem, even for solutions near equilibrium. Our work gives
the first rigorous proof of the uniqueness among solutions that are only
required to be locally Lipschitz; in particular, it holds for solutions far
from equilibrium states.
