Existence And Regularity Of Solutions Of A Phase Field Model For Solidification With Convection Of Pure Materials In Two Dimensions

dc.creatorBoldrini J.L.
dc.creatorVaz C.L.D.
dc.date2003
dc.date2015-06-30T17:30:17Z
dc.date2015-11-26T14:08:55Z
dc.date2015-06-30T17:30:17Z
dc.date2015-11-26T14:08:55Z
dc.date.accessioned2018-03-28T21:09:29Z
dc.date.available2018-03-28T21:09:29Z
dc.identifier
dc.identifierElectronic Journal Of Differential Equations. , v. 2003, n. , p. 1 - 25, 2003.
dc.identifier10726691
dc.identifier
dc.identifierhttp://www.scopus.com/inward/record.url?eid=2-s2.0-3042643009&partnerID=40&md5=30d91b2c4e19cd1241472690d20e358e
dc.identifierhttp://www.repositorio.unicamp.br/handle/REPOSIP/102343
dc.identifierhttp://repositorio.unicamp.br/jspui/handle/REPOSIP/102343
dc.identifier2-s2.0-3042643009
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/1241118
dc.descriptionWe study the existence and regularity of weak solutions of a phase field type model for pure material solidification in presence of natural convection. We assume that the non-stationary solidification process occurs in a two dimensional bounded domain. The governing equations of the model are the phase field equation coupled with a nonlinear heat equation and a modified Navier-Stokes equation. These equations include buoyancy forces modelled by Boussinesq approximation and a Carman-Koseny term to model the flow in mushy regions. Since these modified Navier-Stokes equations only hold in the non-solid regions, which are not known a priori, we have a free boundary-value problem.
dc.description2003
dc.description
dc.description1
dc.description25
dc.descriptionAnderson, D.M., McFadden, G.B., Wheeler, A.A., Diffusive-interface methods in fluid mechanics (1998) Annual Review of Fluid Mechanics, 30, pp. 139-165. , Palo Alto, CA
dc.descriptionBeckermann, C., Diepers, H.-J., Steinbach, I., Karma, A., Tong, X., Modeling melt convection in phase-field simulations of solidification (1999) Journal of Computational Physics, 154, pp. 468-496
dc.descriptionBlanc, Ph., Gasser, L., Rappaz, J., Existence for a stationary model of binary alloy solidification (1995) Math. Modelling. Num. Anal., 29 (6), pp. 687-699
dc.descriptionCaginalp, G., Jones, J., A derivation and analysis of phase field models of thermal alloys (1995) Annal. Phys., 237, pp. 66-107
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., Xie, W., Phase-field and sharp-interface alloy models (1993) Phys. Rev. E, 48 (3), pp. 1897-1999
dc.descriptionCaginalp, G., Stefan and Hele-Shaw type models as asymption limits of the phase-field equations (1989) Phys. Rev. A, 39 (11), pp. 5887-5896
dc.descriptionCaginalp, G., An Analysis of phase field model of a free boundary (1986) Arch. Rat. Mech. Anal., 92, pp. 205-245
dc.descriptionCannon, J.R., DiBenedetto, E., Knigthly, G.H., The bidimensional Stefan problem with convection time dependent case (1983) Comm. Partial. Diff. Eqs., 8 (14), pp. 1549-1604
dc.descriptionCannon, J.R., DiBenedetto, E., Knightly, G.H., The steady state Stefan problem with convection (1980) Arch. Rat. Mech. Anal., 73, pp. 79-97
dc.descriptionCoriell, S.R., Cordes, M.R., Boettinger, W.J., Sekerka, R.F., Effects of gravity on coupled convective and interfacial instabilities during directional solidification (1980) J. Cryst. Growth, 49 (13)
dc.descriptionDavis, S.H., Hydrodynamic interations in directional solidification (1990) J. Fluid Mech., 212 (241)
dc.descriptionDeimling, K., (1984) Nonlinear Functional Analysis, , Springer-Verlag
dc.descriptionDiBenedetto, E., O'Leray, M., Three-dimensional conduction-convection problems with change of phase (1993) Arch. Rat. Mech. Anal., 123, pp. 99-116
dc.descriptionDiBenedetto, E., Friedman, A., Conduction-convection problems with change of phase (1986) J. Diff. Eqs., 62, pp. 129-185
dc.descriptionDiepers, H.-J., Beckermann, C., Steinbach, I., Simulation of convection and ripening in a binary alloy mush using the phase-field method (1999) Acta. Mater., 47 (13), pp. 3663-3678
dc.descriptionFix, G.J., Phase field methods for free boundary problems (1983) Free Boundary Problems: Theory and Applications, pp. 580-589. , A. Fasano, M. Primicerio (Eds), Pitman, Boston
dc.descriptionHoffman, K.H., Jiang, L., Optimal control a phase field model for solidification (1992) Numer. Funct. Anal. Optimiz., 13 (1-2), pp. 11-27
dc.descriptionKobayshi, R., Modeling and numerical simulation of dentritic crystal growth (1993) Phys. D, 63, pp. 410-479
dc.descriptionO'Leray, M., Analysis of the mushy region in conduction-convection problems with change of phase (1997) Elect. Journal. Diff. Eqs., 1997 (4), pp. 1-14
dc.descriptionLadyzenskaja, O.A., Solonnikov, V.A., Ural'ceva, N.N., (1968) Linear and Quasilinear Equations of Parabolic Type, , American Mathematical Society, Providence
dc.descriptionLions, J.L., (1969) Quelques Méthodes de Resolution de Problèmes aux Limites Non Linéaires, , Dunod-Gauthier-Villars, Paris
dc.descriptionMorosanu, C., Motreanu, D., A generalized phase-field system (1999) Journal of Math. Anal. Appl., 237, pp. 515-540
dc.descriptionPericleous, K.A., Cross, M., Moran, G., Chow, P., Chan, K.S., Free surface Navier-Stokes flows with simultaneous heat tranfer and solidification/melting (1996) Adv. Comput. Math., 6, pp. 295-308
dc.descriptionPenrose, O., Fife, P.C., On the relation between the standard phase-field model and a thermodynamically consistent phase-field model (1993) Phys. D, 69, pp. 107-113
dc.descriptionPenrose, O., Fife, P.C., Thermodynamically consistent models of phase-field type for the kinetic phase transitions (1990) Phys D, 43, pp. 44-62
dc.descriptionSimon, J., Compact sets in the space Lp(0, T
dc.descriptionB) (1987) Annali di Matematica Pura ed Applicata, 146, pp. 65-96. , Serie Quarta
dc.descriptionTemam, R., (1977) Navier-Stokes Equations, Theory and Numerical Analysis, , North-Holland Publishing Company
dc.descriptionVaz, C.L.D., (2000) Análise de um Modelo Matemático de Condução-Conveçcão do Tipo Campo de Fases para Solidificação, , Ph.D. Thesis, Universidade Estadual de Campinas, Brazil
dc.descriptionVoller, V.R., Prakash, C., A fixed grid numerical modelling methodology for convection-diffusion mushy region phase-change problems (1987) Int. J. Mass. Tranfer, 30 (8), pp. 1709-1719
dc.descriptionVoller, V.R., Cross, M., Markatos, N.C., An enthalpy method for convection/diffusion phase field models of solidification (1987) Int. J. Num. Methods. Eng., 24 (1), pp. 271-284
dc.languageen
dc.publisher
dc.relationElectronic Journal of Differential Equations
dc.rightsaberto
dc.sourceScopus
dc.titleExistence And Regularity Of Solutions Of A Phase Field Model For Solidification With Convection Of Pure Materials In Two Dimensions
dc.typeArtículos de revistas


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