[Étude analytique et numérique de quelques problèmes à frontière libre et modèles de champ de phase]
;
Elliott, C. ;
Rakotoson, Jean-Michel ;
Abergel, Frédéric ;
Bonami, Aline ;
Hilhorst, Danielle ;
Temam, Roger
@phdthesis{BJHTUP11_1995__0408__P0_0,
author = {Dupaix, Cedric},
title = {Analytical and numerical study of some free boundary value problems and phase field models},
series = {Th\`eses d'Orsay},
publisher = {Universit\'e de Paris-Sud Centre d'Orsay},
number = {408},
year = {1995},
language = {en},
url = {http://archive.numdam.org/item/BJHTUP11_1995__0408__P0_0/}
}
TY - BOOK AU - Dupaix, Cedric TI - Analytical and numerical study of some free boundary value problems and phase field models T3 - Thèses d'Orsay PY - 1995 IS - 408 PB - Université de Paris-Sud Centre d'Orsay UR - http://archive.numdam.org/item/BJHTUP11_1995__0408__P0_0/ LA - en ID - BJHTUP11_1995__0408__P0_0 ER -
Dupaix, Cedric. Analytical and numerical study of some free boundary value problems and phase field models. Thèses d'Orsay, no. 408 (1995), 148 p. http://numdam.org/item/BJHTUP11_1995__0408__P0_0/
[1] and , A mathematical theory for viscous, free-surface flows over a perturbed plane, Arch. Rat. Mech. Anal. 118 (1992), 71-93. | MR | Zbl | DOI
[2] , and , Finite dimensional exponential attractor for the phase field model, Appl. Anal. 49 (1993), 197-212. | MR | Zbl | DOI
[3] , Stefan and Hele-Shaw type models as asymptotic limits of the phase-field equations, Phys. Rev. A 39 n.11 (1989), 5887-5896. | MR | Zbl | DOI
[4] and , Viscous Thermocapillary Convection at High Marangoni Number, J. Fluid. Mech. 135 (1983), 175-188. | Zbl | DOI
[5] , A singular perturbation of the Cahn-Hilliard equation, Asym. Anal. 4 (1991), 161-185. | MR | Zbl
[6] and , On the Cahn-Hilliard equation with a logarithmic free energy, prépublication. | Zbl | DOI
[7] and , The viscous Cahn-Hilliard equation, à paraître. | Zbl
[8] and , Upper semicontinuity of the attractor for a singularly perturbed hyperbolic equation, J. Diff. Eq. 73 (1988), 197-214. | MR | Zbl | DOI
[9] and , Numerical approach to interfacial dynamics, Proceedings of the Workshop on Nonlinear Partial Differential Equations and Applications, 1989.
[10] and , Weighted Spaces with Nonhomogeneous Norms and Boundary Value Problems in Domains with Conical Points, AMS Trans. 123 (1984), 89-108. | Zbl
[11] , On the viscous Cahn-Hilliard equation, Material Instabilities in Continuum Mechanics and Related Mathematical Problems, ed J. Ball, Clarendon-Press, 1988. | MR | Zbl
[12] and , Modeling crystal growth in a diffusion field using fully-facetted interfaces, J. Comput. Phys. 114 (1994), 113-128. | MR | Zbl | DOI
[13] , Surface-Tension Driven Flow in Crystal Growth Melts, Crystals Growth, Properties, and Applications, 11 (1988), Springer Verlag.
[14] , Solvability of a problem on a plane motion of a heavy viscous incompressible capillary liquid partially filling a container, Math. USSR Izves. 14 n.1 (1980), 193-221. | Zbl | DOI
[15] , On the Stokes Equations in Domains with non-smooth Boundaries and on Viscous Incompressible Flow with a Free Surface, Nonlinear Partial Differential Equations and Applications, Collège de France Seminar III (1980-81). | MR | Zbl
[16] , The Cahn-Hilliard equation as limit of the phase-field equations, to appear in Quart. Appl. Math. | MR | Zbl | DOI
[17] , Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Appl. Math. Sci. 68, Springer-Verlag, New-York, 1988. | MR | Zbl
[1] , A geometric approach to the study of stationary free surface flows for viscous liquids, Proceeding of the Royal Society of Edinbourgh, 1993. | MR | Zbl
[2] and , A mathematical theory for viscous, free-surface flows over a perturbed plane, Arch. Rat. Mech. and Ana. 118 (1992), 71-93. | MR | Zbl | DOI
[3] , Rôle de la tension superficielle dans la convection de Bénard, M2AN 24 No2 (1990), 153-175. | MR | Zbl | Numdam | DOI
[4] , Ecoulement Marangoni-Rayleigh induit par un flux thermique sur la surface libre, Thèse de l'Université Paris 11 (1991).
[5] , Operational Mathematics, Mac Graw-Hill International Student Edition. | MR | Zbl
[6] and , Theory of Ordinary Differential Equations, Mac Graw-Hill Ed. | MR | Zbl
[7] and , Viscous Thermocapillary Convection at High Marangoni Number, J. Fluid. Mech. 135 (1983), 175-188. | Zbl | DOI
[8] , Equilibrium Capilary Surfaces, Grundlehren der Mathematischen Wissenschaften 284, Springer Verlag. | MR | Zbl
[9] , Boundary Value Problems for Surfaces of Prescribed Mean Curvature, J. Math. Pures et Appl. 58 (1979), 75-109. | MR | Zbl
[10] , Ordinary Differential Equations, Dover Publications, Inc. | MR | Zbl | JFM
[11] et , Physique Théorique. Mécanique des Fluides, Ed. MIR Moscou 1971. | Zbl
[12] , Structures Dissipatives, Chaos et Turbulence, Collection Aléa Saclay.
[13] and , Weighted Spaces with Nonho- mogeneous Norms and Boundary Value Problems in Domains with Conical Points, AMS Trans. 123 (1984), 89-108. | Zbl
[14] , Surface-Tension Driven Flow in Crystal Growth Melts, Crystals Growth, Properties, and Applications 11 (1988), Springer Verlag.
[15] , Solvability of a problem on a plane motion of a heavy viscous incompressible capillary liquid partially filling a container, Math. USSR Izves. 14 n.1 (1980), 193-221. | Zbl | DOI
[16] , On the Stokes Equations in Domains with nonsmooth Boundaries and on Viscous Incompressible Flow with a Free Surface, Nonlinear Partial Differential Equations and Application, College de France Seminar III (Paris 1980-81). | MR | Zbl
[1] , and , On a dissolution-growth problem with surface tension in the neighborhood of a stationary solution, SIAM J. Math. Anal. Vol. 24, No. 2 (1993), 299-316. | MR | Zbl | DOI
[2] , , and , Local existence and uniqueness of a Stefan problem with surface tension, to appear. | MR | Zbl | DOI
[3] and , Multiphase thermomechanics with interfacial structure 2. Evolution of an isothermal interface, Arch. Rat. Mech. Anal., 108 (4) (1986), 199-241. | MR
[4] , and , Philo. Trans. R. Soc. London, Ser. A (1951), 243-299.
[5] and , Phase field computations of singleneedle crystals, crystal growth, and motion by mean curvature , SIAM J. Sci. Comput. Vol. 15, No. 1 (1994), 106-126. | MR | Zbl | DOI
[6] and , Multiplicity and stability analysis in a free boundary problem arising from a dissolution-growth process, J. of Colloid and Interface Science Vol. 121 (1988), 426-439. | DOI
[7] and , Dissolution-croissance de particules : modèle général et nouvelle approche du murissement d'Oswald, Récents Progrès en Génie des Procédés Vol. 7 (1993), 105-110.
[8] and , Numerical approach to interfacial dynamics, Proc. of Workshop on Nonlinear PDE and Appl. (1989).
[9] and , Fronts propagating with curvature- dependent speed : algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics 79 (1988), 12-49. | MR | Zbl | DOI
[10] and , Tension superficielle et adsorption, Edition Desoer, Liège, 1951.
[11] and , Modeling crystal growth in a diffusion field using fully-facetted interfaces, Journal of Computational Physics 114 (1994), 113-128. | MR | Zbl | DOI
[12] and , GMRES : a generalized minimal residual algorithm for solving nonsymetric linear systems, SIAM J. Sci. Stat. Comput. Vol. 10 (1989), 36-52. | MR | Zbl
[13] , Etude théorique et numérique de l'évolution morphologique d'interfaces, Ph. D. Thesis (1994), University of Orsay (France).
[14] , On a dissolution-growth problem with surface tension : local existence and uniqueness, to appear in Applied Math. Letters. | MR | Zbl
[15] , Private communication.
[16] , Numerical algorithms for propagating interfaces : Hamilton-Jacobi equations and conservation laws, J. Differential Geometry, 31 (1990), 131-161. | MR | Zbl | DOI
[17] , and , I- Geometric models of crystal growth, Acta Metall. Mater. Vol. 40, No 7 (1992), 1443-1474. | DOI
[18] , and , II- Mean curvature and weighted mean curvature, Acta Metall. Mater. Vol. 40, No 7 (1992), 1475-1485. | DOI
[19] and , CGSTAB : a more smoothly converging variant of CG-S, Delft University of Technology, 1990.
[1] , and , Finite dimensional exponential attractor for the phase field model, Appl. Anal. 49 (1993), 197-212. | MR | Zbl | DOI
[2] , Stefan and Hele-Shaw type models as asymptotic limits of the phase-field equations, Phys. Rev. A 39 n.11 (1989), 5887-5896. | MR | Zbl | DOI
[3] , A singular perturbation of the Cahn-Hilliard equation, Asym. Anal. 4 (1991), 161-185. | MR | Zbl
[4] , and , Upper-semicontinuity of the attractor for a singularly perturbed phase field model, preprint. | MR | Zbl
[5] , A singularly perturbed phase field model with a logarithmic nonlinearity, preprint. | MR | Zbl
[6] and , Lower semicontinuity of a non-hyperbolic attractor for the viscous Cahn-Hilliard equations, preprint, University of Sussex (1993). | MR | Zbl
[7] and , The viscous Cahn-Hilliard equation Part II : Analysis, preprint SCCM-94-12, Stanford. | MR | Zbl
[8] and , Upper semicontinuity of the attractor for a singularly perturbed hyperbolic equation, J. Diff. Eq. 73 (1988), 197-214. | MR | Zbl | DOI
[9] , Long-time behaviour for a model of phase-field type, to appear in Proc. Roy. Soc. Edinburgh A. | MR | Zbl
[10] , Approximate inertial manifolds for the pattern formation Cahn-Hilliard equation, RAIRO Math. Mod. Num. Anal. 23 n.3 (1989). 463-488. | MR | Zbl | Numdam | DOI
[11] , On the viscous Cahn-Hilliard equation, Material Instabilities in Continuum Mechanics and Related Mathematical Problems, ed J. Ball, Clarendon-Press, 1988. | MR | Zbl
[12] , Compact sets in the space Lp(0, T; B), Ann. Mat. Pura ed Applicata IV, CXLVI (1987), 65-96. | MR | Zbl
[13] , The Cahn-Hilliard equation as limit of the phase-field equations, to appear in Quart. Appl. Math. | MR | Zbl | DOI
[14] , Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Appl. Math. Sci. 68, Springer-Verlag, New-York, 1988. | MR | Zbl
[1] , and , Finite dimensional exponential attractor for the phase field model, Appl. Anal. 49 (1993), 197-212. | MR | Zbl | DOI
[2] and , On the Cahn-Hilliard equation with a logarithmic free energy, preprint. | MR | Zbl | DOI
[3] , and , Upper-semicontinuity of the attractor for a singular perturbation of the viscous Cahn-Hilliard and Cahn-Hilliard equations, preprint. | Zbl
[4] and , A generalised diffusion equation for phase separation of a multi-component mixture with interfacial free energy, preprint.
[5] , Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires, Dunod. | MR | Zbl
[6] , Compact sets in the space Lp(0,T; B), Ann. Mat. Pura ed Applicata IV, CXLVI (1987) 65-96. | MR | Zbl
[7] , Infinite-dimensional dynamical systems in mechanics and physics, Appl. Math. Sci. 68, Springer-Verlag, New-York, 1988. | MR | Zbl
[8] , Navier-Stokes Equations, Theory and Numerical Analysis, 3rd rev. ed., North-Holland, Amsterdam 1984. | MR | Zbl
