Well-posedness for measure transport in a family of nonlocal domain coarsening models
Barbara Niethammer, Robert L. Pego · Indiana University Mathematics Journal · 2005
In the classical Lifshitz-Slyozov-Wagner theory of Ostwald ripening or domain coarsening, the growth law for particle mass yields a transport equation for the size distribution that is nonlinear through the nonlocal dependence of the mean field on the solution. We study the initial-value problem for a physically reasonable class of such models and prove global existence, uniqueness, and continuous dependence on initial data for solutions taking values initially arbitrary in the space of probability measures with finite mass.