The LSW model for domain coarsening: Asymptotic behavior for conserved total mass

In the classical theory of domain coarsening the particles of the coarsenin g phase evolve by diffusional mass transfer with a mean field. We study the longtime behavior of measure-valued solutions with compact support to this model coupled with the constraint of conserved total mass, including mean- field mass. Unlike the case of conserved volume fraction, this system has n o precisely selfsimilar solutions, and sufficiently low supersaturation can lead to the finite-time extinction of all particles. We find a new explici t family of asymptotically selfsimilar solutions, and in case that the larg est particle size is unbounded we establish results similar to the volume-c onserved case, These include necessary criteria for asymptotic self-similar ity, and sensitive dependence of long-time behavior on the distribution of largest particles in the system.