Optimal Control for the Convective Cahn–Hilliard Equation in 2D Case

Zhao, Xiaopeng; Liu, Changchun

doi:10.1007/s00245-013-9234-0

Cited by 60 publications

(46 citation statements)

References 35 publications

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“…A num-ber of papers also investigates optimal control problems for convective Cahn-Hilliard systems (cf. [38,45,46]) and Cahn-Hilliard-Navier-Stokes systems (cf. [20,27,29,30]).…”

Section: Introductionmentioning

confidence: 99%

Optimal distributed control of a diffuse interface model of tumor growth

et al. 2017

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Abstract. In this paper, a distributed optimal control problem is studied for a diffuse interface model of tumor growth which was proposed by . The model consists of a Cahn-Hilliard equation for the tumor cell fraction ϕ coupled to a reaction-diffusion equation for a function σ representing the nutrientrich extracellular water volume fraction. The distributed control u monitors as a right-hand side the equation for σ and can be interpreted as a nutrient supply or a medication, while the cost function, which is of standard tracking type, is meant to keep the tumor cell fraction under control during the evolution. We show that the control-to-state operator is Fréchet differentiable between appropriate Banach spaces and derive the first-order necessary optimality conditions in terms of a variational inequality involving the adjoint state variables.

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“…A num-ber of papers also investigates optimal control problems for convective Cahn-Hilliard systems (cf. [38,45,46]) and Cahn-Hilliard-Navier-Stokes systems (cf. [20,27,29,30]).…”

Section: Introductionmentioning

confidence: 99%

Optimal distributed control of a diffuse interface model of tumor growth

et al. 2017

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“…In this connection, we refer to [29] and [30], where the latter paper deals with the spatially two-dimensional case. The three-dimensional case with a nonlocal potential is studied in [25].…”

Section: Introductionmentioning

confidence: 99%

A Boundary Control Problem for the Viscous Cahn–Hilliard Equation with Dynamic Boundary Conditions

2015

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“…In this connection, we refer to [15,23,27] and to [25,26] which deal with the convective Cahn-Hilliard equation; the case with a nonlocal potential is studied in [20]. There also exist contributions addressing some discretized versions of general Cahn-Hilliard systems, cf.…”

Section: Introductionmentioning

confidence: 99%