Optimal control of a phase field model for solidification

“…Remark 4.2 The mathematical literature on control problems for phase field systems is scarce and usually restricted to the so-called Caginalp model of phase transitions (see, e. g., [11], [9], [10], [18], and the references given there). More general, thermodynamically consistent phase field models were the subject of [13].…”

Section: Remark 41 Thanks To (44) and Tomentioning

confidence: 99%

Analysis and Optimal Boundary Control of a Nonstandard System of Phase Field Equations

2012

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Abstract. We investigate a nonstandard phase field model of Cahn-Hilliard type. The model, which was introduced in [16], describes two-species phase segregation and consists of a system of two highly nonlinearly coupled PDEs. It has been studied recently in [5], [6] for the case of homogeneous Neumann boundary conditions. In this paper, we investigate the case that the boundary condition for one of the unknowns of the system is of third kind and nonhomogeneous. For the resulting system, we show well-posedness, and we study optimal boundary control problems. Existence of optimal controls is shown, and the first-order necessary optimality conditions are derived. Owing to the strong nonlinear couplings in the PDE system, standard arguments of optimal control theory do not apply directly, although the control constraints and the cost functional will be of standard type.

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“…Many authors have been studied the optimal control problem for the reaction diffusion model( [2], [4], [5]). In [6], the optimal control problem for the chemotaxis model studied.…”

Section: Introductionmentioning

confidence: 99%