Non-self-similar behavior in the LSW theory of Ostwald ripening

The classical Lifshitz-Slyozov-Wagner theory of domain coarsening predicts asymptotically self-similar behavior for the size distribution of a dilute system of particles that evolve by diffusional mass transfer with a common mean field. Here we consider the long-time behavior of measure-valued solut ions for systems in which particle size is uniformly bounded, i.e., for ini tial measures of compact support. We prove that the long-time behavior of t he size distribution depends sensitively on the initial distribution of the largest particles in the system. Convergence to the classically predicted smooth similarity solution is impossible if the initial distribution functi on is comparable to any finite power of distance to the end of the support. We give a necessary criterion for convergence to other self-similar soluti ons, and conditional stability theorems for some such solutions. For a dens e set of initial data, convergence to any selfsimilar solution is impossibl e.