Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  investigate optimal boundary control problems for Cahn--Hilliard variational inequalities with a dynamic boundary condition involving double obstacle potentials and the Laplace--Beltrami operator. The cost functional is of standard tracking type, and box constraints for the controls are prescribed.  prove existence of optimal controls and derive first-order necessary conditions of optimality. The general strategy, which follows the lines of the recent approach by Colli, Farshbaf-Shaker, and Sprekels [Appl. Math. Optim., 71 (2015), pp. 1--24] to the (simpler) Allen--Cahn case, is the following:  use the results that re recently established by Colli, Gilardi, and Sprekels [Appl. Math. Optim., Online First DOI:10.1007/s00245-015-9299-z, 2015] for the case of (differentiable) logarithmic potentials and perform a so-called deep quench limit. Using compactness and monotonicity arguments, it is shown that this strategy leads to the desired first-order necessary optimality conditions for t...
['Pierluigi Colli', 'M. Hassan Farshbaf-Shaker', 'Gianni Gilardi', 'Jürgen Sprekels']
I am writing a research paper on a idea Optimal boundary control of a viscous Cahn-Hilliard system with dynamic boundary condition and double obstacle potentials
[{"from": "human", "value": "I am writing a research paper on a idea Optimal boundary control of a viscous Cahn-Hilliard system with dynamic boundary condition and double obstacle potentials"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  investigate optimal boundary control problems for Cahn--Hilliard variational inequalities with a dynamic boundary condition involving double obstacle potentials and the Laplace--Beltrami operator. The cost functional is of standard tracking type, and box constraints for the controls are prescribed.  prove existence of optimal controls and derive first-order necessary conditions of optimality. The general strategy, which follows the lines of the recent approach by Colli, Farshbaf-Shaker, and Sprekels [Appl. Math. Optim., 71 (2015), pp. 1--24] to the (simpler) Allen--Cahn case, is the following:  use the results that re recently established by Colli, Gilardi, and Sprekels [Appl. Math. Optim., Online First DOI:10.1007/s00245-015-9299-z, 2015] for the case of (differentiable) logarithmic potentials and perform a so-called deep quench limit. Using compactness and monotonicity arguments, it is shown that this strategy leads to the desired first-order necessary optimality conditions for t..."}]