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Applicable Analysis
An International Journal
Volume 92, 2013 - Issue 5
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Articles

Optimal control of the convective Cahn–Hilliard equation

Xiaopeng Zhao Department of Mathematics, Jilin University, Changchun 130012, P.R. China
&
Changchun Liu Department of Mathematics, Jilin University, Changchun 130012, P.R. ChinaCorrespondence[email protected]
Pages 1028-1045 | Received 03 Sep 2011, Accepted 20 Nov 2011, Published online: 14 Dec 2011

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Pierluigi Colli & Andrea Signori. (2021) Boundary control problem and optimality conditions for the Cahn–Hilliard equation with dynamic boundary conditions. International Journal of Control 94:7, pages 1852-1869.
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Jiashan Zheng. (2015) Optimal controls of multidimensional modified Swift–Hohenberg equation. International Journal of Control 88:10, pages 2117-2125.
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Articles from other publishers (29)

Gilbert Peralta. (2021) Distributed Optimal Control of the 2D Cahn–Hilliard–Oberbeck–Boussinesq System for Nonisothermal Viscous Two-Phase Flows. Applied Mathematics & Optimization 84:S2, pages 1219-1279.
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Luca Scarpa. (2021) Analysis and Optimal Velocity Control of a Stochastic Convective Cahn–Hilliard Equation. Journal of Nonlinear Science 31:2.
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Cecilia Cavaterra, Elisabetta Rocca & Hao Wu. (2019) Long-Time Dynamics and Optimal Control of a Diffuse Interface Model for Tumor Growth. Applied Mathematics & Optimization 83:2, pages 739-787.
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Jürgen Sprekels & Hao Wu. (2019) Optimal Distributed Control of a Cahn–Hilliard–Darcy System with Mass Sources. Applied Mathematics & Optimization 83:1, pages 489-530.
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Pierluigi Colli, Gianni Gilardi & Jürgen Sprekels. (2018) Optimal Distributed Control of a Generalized Fractional Cahn–Hilliard System. Applied Mathematics & Optimization 82:2, pages 551-589.
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Matthias Ebenbeck & Patrik Knopf. (2020) Optimal control theory and advanced optimality conditions for a diffuse interface model of tumor growth. ESAIM: Control, Optimisation and Calculus of Variations 26, pages 71.
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Matthias Ebenbeck & Patrik Knopf. (2019) Optimal medication for tumors modeled by a Cahn–Hilliard–Brinkman equation. Calculus of Variations and Partial Differential Equations 58:4.
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Bo You & Fang Li. (2019) Optimal distributed control of the Cahn–Hilliard–Brinkman system with regular potential. Nonlinear Analysis 182, pages 226-247.
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Gianni Gilardi & Jürgen Sprekels. (2019) Asymptotic limits and optimal control for the Cahn–Hilliard system with convection and dynamic boundary conditions. Nonlinear Analysis 178, pages 1-31.
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Michele Colturato. (2017) On a Class of Conserved Phase Field Systems with a Maximal Monotone Perturbation. Applied Mathematics & Optimization 78:3, pages 545-585.
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Harald Garcke, Kei Fong Lam & Elisabetta Rocca. (2017) Optimal Control of Treatment Time in a Diffuse Interface Model of Tumor Growth. Applied Mathematics & Optimization 78:3, pages 495-544.
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Pierluigi Colli, Gianni Gilardi & Jürgen Sprekels. (2018) On a Cahn–Hilliard system with convection and dynamic boundary conditions. Annali di Matematica Pura ed Applicata (1923 -) 197:5, pages 1445-1475.
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Pierluigi Colli, Gianni Gilardi & Jürgen Sprekels. (2018) Optimal boundary control of a nonstandard viscous Cahn–Hilliard system with dynamic boundary condition. Nonlinear Analysis 170, pages 171-196.
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Pierluigi Colli, Gianni Gilardi & Jürgen Sprekels. (2018) Optimal Velocity Control of a Viscous Cahn--Hilliard System with Convection and Dynamic Boundary Conditions. SIAM Journal on Control and Optimization 56:3, pages 1665-1691.
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A. R. Appadu, J. K. Djoko & H. H. Gidey. (2017) A priori analysis of multilevel finite volume approximation of 1D convective Cahn–Hilliard equation. Afrika Matematika 28:7-8, pages 1193-1233.
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Pierluigi Colli, Gianni Gilardi, Elisabetta Rocca & J?rgen Sprekels. (2017) Optimal distributed control of a diffuse interface model of tumor growth. Nonlinearity 30:6, pages 2518-2546.
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Cecilia Cavaterra, Elisabetta Rocca & Hao Wu. (2017) Optimal Boundary Control of a Simplified Ericksen?Leslie System for Nematic Liquid Crystal Flows in 2D. Archive for Rational Mechanics and Analysis 224:3, pages 1037-1086.
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A. R. Appadu, J. K. Djoko, H. H. Gidey & J. M. S. Lubuma. (2017) Analysis of multilevel finite volume approximation of 2D convective Cahn?Hilliard equation. Japan Journal of Industrial and Applied Mathematics 34:1, pages 253-304.
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P. Colli, G. Gilardi & J. Sprekels. (2017) Recent Results on the Cahn - Hilliard Equation with Dynamic Boundary Conditions. Bulletin of the South Ural State University. Series "Mathematical Modelling, Programming and Computer Software" 10:1, pages 5-21.
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Pierluigi Colli & Jürgen Sprekels. 2017. Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs. Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs 151 182 .
Pierluigi Colli, Gianni Gilardi & Jürgen Sprekels. (2016) Distributed optimal control of a nonstandard nonlocal phase field system with double obstacle potential. Evolution Equations and Control Theory 6:1, pages 35-58.
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Pierluigi Colli, Gianni Gilardi & J?rgen Sprekels. (2015) A Boundary Control Problem for the Viscous Cahn?Hilliard Equation with Dynamic Boundary Conditions. Applied Mathematics & Optimization 73:2, pages 195-225.
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Sergio Frigeri, Elisabetta Rocca & J?rgen Sprekels. (2016) Optimal Distributed Control of a Nonlocal Cahn--Hilliard/Navier--Stokes System in Two Dimensions. SIAM Journal on Control and Optimization 54:1, pages 221-250.
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Xiaopeng Zhao & Zhen-Hu Ning. (2015) Optimal control problem for the modified Swift-Hohenberg equation in 3D case. Mathematical Methods in the Applied Sciences 38:18, pages 4650-4662.
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XIAOPENG ZHAO. (2015) SPECTRAL APPROXIMATIONS OF ATTRACTORS FOR CONVECTIVE CAHN-HILLIARD EQUATION IN TWO DIMENSIONS. Bulletin of the Korean Mathematical Society 52:5, pages 1445-1465.
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Pierluigi Colli, M. Hassan Farshbaf-Shaker, Gianni Gilardi & J?rgen Sprekels. (2015) Optimal Boundary Control of a Viscous Cahn--Hilliard System with Dynamic Boundary Condition and Double Obstacle Potentials. SIAM Journal on Control and Optimization 53:4, pages 2696-2721.
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E. Rocca & J. Sprekels. (2015) Optimal Distributed Control of a Nonlocal Convective Cahn--Hilliard Equation by the Velocity in Three Dimensions. SIAM Journal on Control and Optimization 53:3, pages 1654-1680.
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Xiufang Zhao & Ning Duan. (2014) Optimal control of the sixth-order convective Cahn-Hilliard equation. Boundary Value Problems 2014:1.
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Xiaopeng Zhao & Changchun Liu. (2014) Optimal Control for the Convective Cahn?Hilliard Equation in 2D Case. Applied Mathematics & Optimization 70:1, pages 61-82.
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