Distributed optimal control of a nonstandard system of phase field equations

Details Distributed optimal control of a nonstandard system of phase field equations Distributed optimal control of a nonstandard system of phase field equations

2011-06-18

arxiv.org/abs/1106.3668v1

Mathematics

Analysis of PDEs

Key words: distributed optimal control, nonlinear phase field systems, first-order necessary optimality conditions

Scientific paper

We investigate a distributed optimal control problem for a phase field model of Cahn-Hilliard type. The model describes two-species phase segregation on an atomic lattice under the presence of diffusion; it has been recently introduced by the same authors in arXiv:1103.4585v1 [math.AP] and consists of a system of two highly nonlinearly coupled PDEs. For this reason, standard arguments of optimal control theory do not apply directly, although the control constraints and the cost functional are of standard type. We show that the problem admits a solution, and we derive the first-order necessary conditions of optimality.

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