Optimal Distributed Control of a Nonlocal Convective Cahn-Hilliard Equation by the Velocity in Three Dimensions
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[1] Ciprian G. Gal,et al. On Nonlocal Cahn–Hilliard–Navier–Stokes Systems in Two Dimensions , 2014, Journal of Nonlinear Science.
[2] H. Petzeltová,et al. Convergence of solutions of a non-local phase-field system , 2010 .
[3] Fredi Tröltzsch,et al. Optimal Control of Three-Dimensional State-Constrained Induction Heating Problems with Nonlocal Radiation Effects , 2011, SIAM J. Control. Optim..
[4] Harald Garcke,et al. Allen-Cahn and Cahn-Hilliard Variational Inequalities Solved with Optimization Techniques , 2012, Constrained Optimization and Optimal Control for Partial Differential Equations.
[5] Cheng Wang,et al. A convergent convex splitting scheme for the periodic nonlocal Cahn-Hilliard equation , 2014, Numerische Mathematik.
[6] M. Grasselli,et al. Global existence of weak solutions to a nonlocal Cahn–Hilliard–Navier–Stokes system , 2011, 1101.3906.
[7] J. Waals. The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density , 1979 .
[8] P. Colli,et al. Analysis and Optimal Boundary Control of a Nonstandard System of Phase Field Equations , 2012, 1201.5541.
[9] Herbert Gajewski,et al. On a nonlocal phase separation model , 2003 .
[10] Xiaopeng Zhao,et al. Optimal control of the convective Cahn–Hilliard equation , 2013 .
[11] J. E. Hilliard,et al. Spinodal decomposition: A reprise , 1971 .
[12] Jürgen Sprekels,et al. Distributed optimal control of a nonstandard system of phase field equations , 2011, Continuum Mechanics and Thermodynamics.
[13] Xiaopeng Zhao,et al. Optimal Control for the Convective Cahn–Hilliard Equation in 2D Case , 2014 .
[14] Joel Lebowitz,et al. Phase Segregation Dynamics in Particle Systems with Long Range Interactions II: Interface Motion , 1997, SIAM J. Appl. Math..
[15] Christian Meyer,et al. State-Constrained Optimal Control of Semilinear Elliptic Equations with Nonlocal Radiation Interface Conditions , 2009, SIAM J. Control. Optim..
[16] Fredi Tröltzsch,et al. Optimal Control of a Semilinear PDE with Nonlocal Radiation Interface Conditions , 2006, SIAM J. Control. Optim..
[17] Hana Petzeltová,et al. Regularity and separation from potential barriers for a non-local phase-field system , 2011 .
[18] Michael Hintermüller,et al. Distributed Optimal Control of the Cahn-Hilliard System Including the Case of a Double-Obstacle Homogeneous Free Energy Density , 2012, SIAM J. Control. Optim..
[19] R. Fornari,et al. Crystallization of 640 kg mc-silicon ingots under traveling magnetic field by using a heater-magnet module , 2013 .
[20] C. M. Elliott,et al. On the Cahn-Hilliard equation with degenerate mobility , 1996 .
[21] J. Lions. Quelques méthodes de résolution de problèmes aux limites non linéaires , 1969 .
[22] J. Simon. Compact sets in the spaceLp(O,T; B) , 1986 .
[23] Non‐local temperature‐dependent phase‐field models for non‐isothermal phase transitions , 2005 .
[24] Peter W. Bates,et al. The Neumann boundary problem for a nonlocal Cahn–Hilliard equation , 2005 .
[25] John W. Cahn,et al. On Spinodal Decomposition , 1961 .