dc.creator | Araruna F.D. | |
dc.creator | Boldrini J.L. | |
dc.creator | Calsavara B.M.R. | |
dc.date | 2014 | |
dc.date | 2015-06-25T18:01:20Z | |
dc.date | 2015-11-26T15:03:01Z | |
dc.date | 2015-06-25T18:01:20Z | |
dc.date | 2015-11-26T15:03:01Z | |
dc.date.accessioned | 2018-03-28T22:13:54Z | |
dc.date.available | 2018-03-28T22:13:54Z | |
dc.identifier | | |
dc.identifier | Applied Mathematics And Optimization. Springer New York Llc, v. 70, n. 3, p. 539 - 563, 2014. | |
dc.identifier | 954616 | |
dc.identifier | 10.1007/s00245-014-9249-1 | |
dc.identifier | http://www.scopus.com/inward/record.url?eid=2-s2.0-84911004607&partnerID=40&md5=35f32dcb906d795f780a3512173ce47d | |
dc.identifier | http://www.repositorio.unicamp.br/handle/REPOSIP/87553 | |
dc.identifier | http://repositorio.unicamp.br/jspui/handle/REPOSIP/87553 | |
dc.identifier | 2-s2.0-84911004607 | |
dc.identifier.uri | http://repositorioslatinoamericanos.uchile.cl/handle/2250/1256515 | |
dc.description | Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) | |
dc.description | We 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.description | 70 | |
dc.description | 3 | |
dc.description | 539 | |
dc.description | 563 | |
dc.description | CAPES; Conselho Nacional de Desenvolvimento Científico e Tecnológico; CNPq; Conselho Nacional de Desenvolvimento Científico e Tecnológico; FAPESP; Conselho Nacional de Desenvolvimento Científico e Tecnológico | |
dc.description | Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) | |
dc.description | Benincasa, 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.description | Benincasa, 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.description | Benincasa, 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.description | Moroşanu, C., Boundary optimal control problem for the phase-field transition system using fractional steps method (2003) Control Cybern., 32 (1), pp. 5-32 | |
dc.description | Moroşanu, 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.description | Cheng, M., Warren, J.A., An efficient algorithm for solving the phase field crystal model (2008) J. Comput. Phys., 227 (12), pp. 6241-6248 | |
dc.description | Hamide, 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.description | He, 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.description | Moroşanu, 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.description | Rosam, 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.description | Sun, 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.description | Tan, 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.description | Zhao, 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.description | Ahmad, 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.description | Boldrini, 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.description | Caginalp, G., An analysis of phase field model of a free boundary (1986) Arch. Ration. Mech. Anal., 92, pp. 205-245 | |
dc.description | Caginalp, 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.description | Caginalp, 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.description | Caginalp, G., Jones, J., A derivation and analysis of phase field models of thermal alloys (1995) Annal. Phys., 237, pp. 66-107 | |
dc.description | Cherfils, 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.description | Colli, P., Grasselli, M., Ito, A., On a parabolic–hyperbolic Penrose–Fife phase-field system (2002) Electron. J. Differ. Equ., 100, pp. 1-30 | |
dc.description | Gilardi, 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.description | Gilardi, 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.description | Jiménez-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.description | Karma, A., Phase-field models of microstructural pattern formation (2003) Thermodyn. Microstruct. Plast. NATO Sci. Ser. II Math. Phys. Chem., 108, pp. 65-89 | |
dc.description | Krejcí, 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.description | Krejcí, 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.description | Laurençot, 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.description | McFadden, 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.description | Moroşanu, C., Analysis and optimal control of phase-field transition system (2003) Nonlinear Funct. Anal. Appl., 8 (3), pp. 433-460 | |
dc.description | Nestler, B., Garcke, H., Stinner, B., Multicomponent alloy solidification: phase-field modeling and simulations (2005) Phys. Rev. E, 71 (4), pp. 1-6 | |
dc.description | Penrose, 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.description | Planas, G., Existence of solutions to a phase-field model with phase-dependent heat absorption (2007) Electron. J. Differ. Equ., 28, pp. 1-12 | |
dc.description | Stinner, 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.description | Aizicovici, S., Feireisl, E., Long-time stabilization of solutions to a phase-field model with memory (2001) J. Evol. Equ., 1, pp. 69-84 | |
dc.description | Aizicovici, 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.description | Bates, P.W., Zheng, S., Inertial manifolds and inertial sets for phase-field equations (1992) J. Dyn. Differ. Equ., 4, pp. 375-397 | |
dc.description | Brochet, D., Chen, X., Hilhorst, D., Finite dimensional exponential attractor for the phase-field model (1993) Appl. Anal., 49, pp. 197-212 | |
dc.description | Jiang, 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.description | Kapustyan, 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.description | Röger, 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.description | Sprekels, 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.description | Hoffman, K., Jiang, L., Optimal control of a phase field model for solidification (1992) Numer. Funct. Anal. Optim., 13, pp. 11-27 | |
dc.description | Wang, L., Wang, G., The optimal time control of a phase-field system (2003) SIAM J. Control Optim., 42 (4), pp. 1483-1508 | |
dc.description | Barbu, V., Local controllability of the phase field system (2002) Nonlinear Anal., 50 (3), pp. 363-372 | |
dc.description | Ammar-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.description | González-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.description | Cao, 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.description | Adams, R., (1975) Sobolev Spaces, , Academic Press, New York: | |
dc.description | Ladyzenskaja, 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.description | Mikhaylov, V.P., (1978) Partial Differential Equations, , Mir Publishers, Moscow: | |
dc.description | Lions, J.L., (1985) Control of Distributed Singular Systems, , Gauthier-Villars, Paris: | |
dc.description | Chae, 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.description | Fabre, C., Puel, J.-P., Zuazua, E., Approximate controllability of the semilinear heat equation (1995) Proc. R. Soc. Edinb., 125 (1), pp. 31-61 | |
dc.description | Doubova, 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.language | en | |
dc.publisher | Springer New York LLC | |
dc.relation | Applied Mathematics and Optimization | |
dc.rights | fechado | |
dc.source | Scopus | |
dc.title | Optimal Control And Controllability Of A Phase Field System With One Control Force | |
dc.type | Artículos de revistas | |