  The LSW model with encounters has been suggested by Lifshitz and Slyozov as a
regularization of their classical mean-field model for domain coarsening to
obtain universal self-similar long-time behavior. We rigorously establish that
an exponentially decaying self-similar solution to this model exist, and show
that this solutions is isolated in a certain function space. Our proof relies
on setting up a suitable fixed-point problem in an appropriate function space
and careful asymptotic estimates of the solution to a corresponding homogeneous
problem.
