dc.creatorAraruna F.D.
dc.creatorBoldrini J.L.
dc.creatorCalsavara B.M.R.
dc.date2014
dc.date2015-06-25T18:01:20Z
dc.date2015-11-26T15:03:01Z
dc.date2015-06-25T18:01:20Z
dc.date2015-11-26T15:03:01Z
dc.date.accessioned2018-03-28T22:13:54Z
dc.date.available2018-03-28T22:13:54Z
dc.identifier
dc.identifierApplied Mathematics And Optimization. Springer New York Llc, v. 70, n. 3, p. 539 - 563, 2014.
dc.identifier954616
dc.identifier10.1007/s00245-014-9249-1
dc.identifierhttp://www.scopus.com/inward/record.url?eid=2-s2.0-84911004607&partnerID=40&md5=35f32dcb906d795f780a3512173ce47d
dc.identifierhttp://www.repositorio.unicamp.br/handle/REPOSIP/87553
dc.identifierhttp://repositorio.unicamp.br/jspui/handle/REPOSIP/87553
dc.identifier2-s2.0-84911004607
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/1256515
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.descriptionWe investigate the relation between optimal control and controllability for a phase field system modeling the solidification process of pure materials in the case that only one control force is used. Such system is constituted of one energy balance equation, with a localized control associated to the density of heat sources and sinks to be determined, coupled with a phase field equation with the classical nonlinearity derived from the two-well potential. We prove that this system has a local controllability property and we establish that a sequence of solutions of certain optimal control problems converges to a solution of such controllability problem.
dc.description70
dc.description3
dc.description539
dc.description563
dc.descriptionCAPES; Conselho Nacional de Desenvolvimento Científico e Tecnológico; CNPq; Conselho Nacional de Desenvolvimento Científico e Tecnológico; FAPESP; Conselho Nacional de Desenvolvimento Científico e Tecnológico
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.descriptionBenincasa, T., Moroşanu, C., Fractional steps scheme to approximate the phase-field transition system with non-homogeneous Cauchy–Neumann boundary conditions (2009) Numer. Funct. Anal. Optim., 30 (3-4), pp. 199-213
dc.descriptionBenincasa, T., Favini, A., Moroşanu, C., A product formula approach to a nonhomogeneous boundary optimal control problem governed by nonlinear phase-field transition system. Part I: a phase-field model (2011) J. Optim. Theory Appl., 148 (1), pp. 14-30
dc.descriptionBenincasa, T., Favini, A., Moroşanu, C., A product formula approach to a nonhomogeneous boundary optimal control problem governed by nonlinear phase-field transition system. Part II: Lie–Trotter product formula (2011) J. Optim. Theory Appl., 148 (1), pp. 14-30
dc.descriptionMoroşanu, C., Boundary optimal control problem for the phase-field transition system using fractional steps method (2003) Control Cybern., 32 (1), pp. 5-32
dc.descriptionMoroşanu, C., The phase-field transition system with non-homogeneous Cauchy–Stefan–Boltzmann and homogeneous Neumann boundary conditions and non-constant thermal conductivity (2013) Nonlinear Anal., 87, pp. 22-32
dc.descriptionCheng, M., Warren, J.A., An efficient algorithm for solving the phase field crystal model (2008) J. Comput. Phys., 227 (12), pp. 6241-6248
dc.descriptionHamide, M., Massoni, E., Bellet, M., Adaptive mesh technique for thermal–metallurgical numerical simulation of arc welding processes (2008) Int. J. Numer. Methods Eng., 73 (5), pp. 624-641
dc.descriptionHe, Q., Kasagi, N., Phase-field simulation of small capillary-number two-phase flow in a microtube (2008) Fluid Dyn. Res., 40 (7-8), pp. 497-509
dc.descriptionMoroşanu, C., Wang, G., State-constrained optimal control for the phase-field transition system (2007) Numer. Funct. Anal. Optim., 28 (3-4), pp. 379-403
dc.descriptionRosam, J., Jimack, P.K., Mullis, A.A., Fully implicit, fully adaptive time and space discretization method for phase-field simulation of binary alloy solidification (2007) J. Comput. Phys., 225 (2), pp. 1271-1287
dc.descriptionSun, Y., Beckermann, C., (2005) Phase-Field Simulation of Two-Phase Micro-flows in a Hele-Shaw Cell, Computational Methods in Multiphase Flow III, WIT Trans. Eng. Sci., , 50, WIT Press, Southampton:
dc.descriptionTan, Z., Huang, Y., An alternating Crank–Nicolson method for the numerical solution of the phase-field equations using adaptive moving meshes (2008) Int. J. Numer. Methods Fluids, 56 (9), pp. 1673-1693
dc.descriptionZhao, P., Heinrich, J.C., Poirier, D.R., Dendritic solidification of binary alloys with free and forced convection (2005) Int. J. Numer. Methods Fluids, 49 (3), pp. 233-266
dc.descriptionAhmad, N.A., Wheeler, A.A., Boettinger, W.J., Mcfadden, G.B., Solute trapping and solute drag in a phase-field model of rapid solidification (1998) Phys. Rev. E Stat. Phys. Plasmas Fluids, 58 (3B), pp. 3436-3450
dc.descriptionBoldrini, J.L., Vaz, C.L.D., Existence and regularity of solutions of a phase field model for solidification with convection of pure materials in two dimensions (2003) Electron. J. Differ. Equ., 109, pp. 1-25
dc.descriptionCaginalp, G., An analysis of phase field model of a free boundary (1986) Arch. Ration. Mech. Anal., 92, pp. 205-245
dc.descriptionCaginalp, G., Stefan and Hele-Shaw type models as assymptotic limits of the phase-field equations (1989) Phys. Rev. A, 39 (11), pp. 5887-5896
dc.descriptionCaginalp, G., Phase field computations of single-needle crystals, crystal growth and motion by mean curvature (1994) SIAM J. Sci. Comput., 15 (1), pp. 106-126
dc.descriptionCaginalp, G., Jones, J., A derivation and analysis of phase field models of thermal alloys (1995) Annal. Phys., 237, pp. 66-107
dc.descriptionCherfils, L., Gatti, S., Miranville, A., Existence of global solutions to the Caginalp phase-field system with dynamic boundary conditions and singular potentials (2008) J. Math. Anal. Appl., 343 (1), pp. 557-566
dc.descriptionColli, P., Grasselli, M., Ito, A., On a parabolic–hyperbolic Penrose–Fife phase-field system (2002) Electron. J. Differ. Equ., 100, pp. 1-30
dc.descriptionGilardi, G., Marson, A., On a Penrose–Fife type system with Dirichlet boundary conditions for temperature (2003) Math. Methods Appl. Sci., 26 (15), pp. 1303-1325
dc.descriptionGilardi, G., Rocca, E., Convergence of phase field to phase relaxation models governed by an entropy equation with memory (2006) Math. Methods Appl. Sci., 29 (18), pp. 2149-2179
dc.descriptionJiménez-Casas, A., Invariant regions and global existence for a phase field model (2008) Discret. Contin. Dyn. Syst. Ser. S, 1 (2), pp. 273-281
dc.descriptionKarma, A., Phase-field models of microstructural pattern formation (2003) Thermodyn. Microstruct. Plast. NATO Sci. Ser. II Math. Phys. Chem., 108, pp. 65-89
dc.descriptionKrejcí, P., Rocca, E., Sprekels, J., Non-local temperature-dependent phase-field models for non-isothermal phase transitions (2007) J. Lond. Math. Soc., 76 (1), pp. 197-210
dc.descriptionKrejcí, P., Sprekels, J., Stefanelli, U., One-dimensional thermo-visco-plastic processes with hysteresis and phase transitions (2003) Adv. Math. Sci. Appl., 13 (2), pp. 695-712
dc.descriptionLaurençot, P., Schimperna, G., Stefanelli, U., Global existence of a strong solution to the one-dimensional full model for irreversible phase transitions (2002) J. Math. Anal. Appl., 271 (2), pp. 426-442
dc.descriptionMcFadden, G.B., Wheeler, A.A., Anderson, D.M., Thin interface asymptotics for an energy/entropy approach to phase-field models with unequal conductivities (2000) Phys. D, 144 (2), pp. 154-168
dc.descriptionMoroşanu, C., Analysis and optimal control of phase-field transition system (2003) Nonlinear Funct. Anal. Appl., 8 (3), pp. 433-460
dc.descriptionNestler, B., Garcke, H., Stinner, B., Multicomponent alloy solidification: phase-field modeling and simulations (2005) Phys. Rev. E, 71 (4), pp. 1-6
dc.descriptionPenrose, O., Fife, P.C., Thermodynamically consistent models of phase field type for the kinetics of phase transitions (1990) Phys. D, 43, pp. 44-62
dc.descriptionPlanas, G., Existence of solutions to a phase-field model with phase-dependent heat absorption (2007) Electron. J. Differ. Equ., 28, pp. 1-12
dc.descriptionStinner, B., Weak solutions to a multi-phase field system of parabolic equations related to alloy solidification (2007) Adv. Math. Sci. Appl., 17 (2), pp. 589-638
dc.descriptionAizicovici, S., Feireisl, E., Long-time stabilization of solutions to a phase-field model with memory (2001) J. Evol. Equ., 1, pp. 69-84
dc.descriptionAizicovici, S., Feireisl, E., Issard-Roch, F., Long time convergence of solutions to a phase-field system (2001) Math. Methods Appl. Sci., 24, pp. 277-287
dc.descriptionBates, P.W., Zheng, S., Inertial manifolds and inertial sets for phase-field equations (1992) J. Dyn. Differ. Equ., 4, pp. 375-397
dc.descriptionBrochet, D., Chen, X., Hilhorst, D., Finite dimensional exponential attractor for the phase-field model (1993) Appl. Anal., 49, pp. 197-212
dc.descriptionJiang, J., Convergence to equilibrium for a parabolic–hyperbolic phase field model with Cattaneo heat flux law (2008) J. Math. Anal. Appl., 341 (1), pp. 149-169
dc.descriptionKapustyan, A.V., Melnik, V.S., Valero, J., Attractors of multivalued dynamical processes generated by phase-field equations (2003) Int. J. Bifurc. Chaos Appl. Sci. Eng., 13 (7), pp. 1969-1983
dc.descriptionRöger, M., Tonegawa, Y., Convergence of phase-field approximations to the Gibbs–Thomson law (2008) Calc. Var. Partial Differ. Equ., 32 (1), pp. 111-136
dc.descriptionSprekels, J., Zheng, S., Global existence and asymptotic behaviour for a nonlocal phase-field model for non-isothermal phase transitions (2003) J. Math. Anal. Appl., 279 (1), pp. 97-110
dc.descriptionHoffman, K., Jiang, L., Optimal control of a phase field model for solidification (1992) Numer. Funct. Anal. Optim., 13, pp. 11-27
dc.descriptionWang, L., Wang, G., The optimal time control of a phase-field system (2003) SIAM J. Control Optim., 42 (4), pp. 1483-1508
dc.descriptionBarbu, V., Local controllability of the phase field system (2002) Nonlinear Anal., 50 (3), pp. 363-372
dc.descriptionAmmar-Khodja, F., Benabdallah, A., Dupaix, C., Kostin, I., Controllability to the trajectories of phase-field models by one control force (2003) SIAM J. Control Optim., 42 (5), pp. 1661-1680
dc.descriptionGonzález-Burgos, M., Pérez-García, R., Controllability results for some nonlinear coupled parabolic systems by one control force (2006) Asymptot. Anal., 46 (2), pp. 123-162
dc.descriptionCao, Y., Numerical approximations of exact controllability problems by optimal control problems for parabolic differential equations (2001) Appl. Math. Comput., 119 (2-3), pp. 127-145
dc.descriptionAdams, R., (1975) Sobolev Spaces, , Academic Press, New York:
dc.descriptionLadyzenskaja, O.A., Solonnikov, V.A., Ural’ceva, N.N., (1968) Linear and Quasilinear Equations of Parabolic Type, Translations of Mathematical Monographs, , 23, American Mathematical Society, Providence:
dc.descriptionMikhaylov, V.P., (1978) Partial Differential Equations, , Mir Publishers, Moscow:
dc.descriptionLions, J.L., (1985) Control of Distributed Singular Systems, , Gauthier-Villars, Paris:
dc.descriptionChae, D., Imanuvilov, O.Y., Kim, S.M., Exact controllability for semilinear parabolic equations with Neumann boundary conditions (1996) J. Dyn. Control Syst., 2 (4), pp. 449-483
dc.descriptionFabre, C., Puel, J.-P., Zuazua, E., Approximate controllability of the semilinear heat equation (1995) Proc. R. Soc. Edinb., 125 (1), pp. 31-61
dc.descriptionDoubova, A., Fernández-Cara, E., González-Burgos, M., Zuazua, E., On the controllability of parabolic systems with a nonlinear term involving the state and the gradient (2002) SIAM J. Control Optim., 41 (3), pp. 798-819
dc.languageen
dc.publisherSpringer New York LLC
dc.relationApplied Mathematics and Optimization
dc.rightsfechado
dc.sourceScopus
dc.titleOptimal Control And Controllability Of A Phase Field System With One Control Force
dc.typeArtículos de revistas


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