Optimal Control of Mean Field Models for Phase Transitions

Abstract

AbstractVarious models prescribe precipitation due to phase transitions. On a macroscopic level the well-known Lifshitz-Slyozov-Wagner (LSW) models and its discrete analogons, so-called mean field models, prescribe the size evolution of precipitates for two-phase systems. For industrial tasks it is desirable to control the resulting distribution of droplet volume. While there are optimal control results for phase-field models and for nonlinear hyperbolic conservation laws, it seems that control problems for LSW equations and mean field models, including measure-valued solutions or switching conditions, have not been considered so far. We formulate the model for this important new control problem and present first numerical results.