Optimal Control of Mean Field Models for Phase Transitions
Collection editors:
Troch, Inge; Breitenecker, Felix
Title of conference publication:
IFAC Mathematical Modelling - 7th Vienna International Conference on Mathematical Modelling 2012
Organizer (entity):
International Federation of Automatic Control (IFAC)
Conference title:
Vienna International Conference on Mathematical Modelling (7., 2012, Wien)
Conference title:
MATHMOD 2012
Venue:
Wien, Österreich
Year of conference:
2012
Date of conference beginning:
14.02.2012
Date of conference ending:
17.02.2012
Publishing institution:
IFAC
Year:
2013
Pages from - to:
1107-1111
Language:
Englisch
Keywords:
optimal control,process control,nonlinear control systems,end point control,partial differential equations,characteristic curves,differential algebraic equations (DAE) mathematical models,phase transition,LSW equation
Abstract:
Various 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. «
Various 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... »