Bibliography related to the project

ACI Propagating phase boundaries and capillary fluid

This list is not supposed to be exhaustive. However, any additional suggestion will be considered. Please then send an e-mail to benzoni@umpa.ens-lyon.fr with the complete reference, possibly in BibTeX format, and any relevant link.

References

[1]

D. M. Anderson, G. B. McFadden, and A. A. Wheeler. Diffuse-interface methods in fluid mechanics. In Annual review of fluid mechanics, Vol. 30, pages 139-165. Annual Reviews, Palo Alto, CA, 1998.

[2]

S. Benzoni-Gavage. Stability of multi-dimensional phase transitions in a van der Waals fluid. Nonlinear Analysis T.M.A., 31(1/2):243-263, 1998.

[3]

S. Benzoni-Gavage. Stability of subsonic planar phase boundaries in a van der Waals fluid. Arch. Rational Mech. Anal., 150(1):23-55, 1999.

[4]

S. Benzoni-Gavage. Linear stability of propagating phase boundaries in capillary fluids. Physica D, 155:235-273, 2001.

[5]

Franck Boyer. Mathematical study of multi-phase flow under shear through order parameter formulation. Asymptot. Anal., 20(2):175-212, 1999.

[6]

Franck Boyer. Nonhomogeneous Cahn-Hilliard fluids. Ann. Inst. H. Poincaré Anal. Non Linéaire, 18(2):225-259, 2001.

[7]

Franck Boyer. A theoretical and numerical model for the study of incompressible mixture flows. Computers & Fluids, 31:41-68, 2002.

[8]

M. Brouillette and B. Sturtevant. Experiments on the Richtmyer-Meshkov instability: single-scale perturbations on a continuous interface. J. Fluid Mech., 263:271-292, 1994.

[9]

P. Casal and H. Gouin. Équations du mouvement des fluides thermocapillaires. C. R. Acad. Sci. Paris Sér. II Méc. Phys. Chim. Sci. Univers Sci. Terre, 306(2):99-104, 1988.

[10]

Raphaël Danchin and Benoît Desjardins. Existence of solutions for compressible fluid models of Korteweg type. Ann. Inst. H. Poincaré Anal. Non Linéaire, 18(1):97-133, 2001.

[11]

D. L. Denny and R. L. Pego. Models of low-speed flow for near-critical fluids with gravitational and capillary effects. Quart. Appl. Math., 58(1):103-125, 2000.

[12]

R.E. Duff, F.H. Harlow, and C.W. Hirt. Effects of diffusion on interface instability between gases. Phys. Fluids, 5:417-425, 1962.

[13]

J. E. Dunn and J. Serrin. On the thermomechanics of interstitial working. Arch. Rational Mech. Anal., 88(2):95-133, 1985.

[14]

S. Gavrilyuk and H. Gouin. Symmetric form of governing equations for capillary fluids. In Trends in applications of mathematics to mechanics (Nice, 1998), pages 306-311. Chapman & Hall/CRC, Boca Raton, FL, 2000.

[15]

S. L. Gavrilyuk. Solitary waves in bubbly liquids are linearly unstable. European J. Mech. B Fluids, 15(1):37-53, 1996.

[16]

H. Gouin and M. Slemrod. Stability of spherical isothermal liquid-vapor interfaces. Meccanica, 30(3):305-319, 1995.

[17]

Morton E. Gurtin. Toward a nonequilibrium thermodynamics of two-phase materials. Arch. Rational Mech. Anal., 100(3):275-312, 1988.

[18]

Morton E. Gurtin. On a nonequilibrium thermodynamics of capillarity and phase. Quart. Appl. Math., 47(1):129-145, 1989.

[19]

R. Hagan and M. Slemrod. The viscosity-capillarity criterion for shocks and phase transitions. Arch. Rational Mech. Anal., 83(4):333-361, 1983.

[20]

H. Hattori and De Ning Li. Solutions for two-dimensional system for materials of Korteweg type. SIAM J. Math. Anal., 25(1):85-98, 1994.

[21]

H. Hattori and Dening Li. Global solutions of a high-dimensional system for Korteweg materials. J. Math. Anal. Appl., 198(1):84-97, 1996.

[22]

Harumi Hattori and Dening Li. The existence of global solutions to a fluid dynamic model for materials for Korteweg type. J. Partial Differential Equations, 9(4):323-342, 1996.

[23]

Richard James and David Kinderlehrer. Theory of diffusionless phase transitions. In PDEs and continuum models of phase transitions (Nice, 1988), pages 51-84. Springer, Berlin, 1989.

[24]

Richard D. James. The propagation of phase boundaries in elastic bars. Arch. Rational Mech. Anal., 73(2):125-158, 1980.

[25]

Richard D. James. A relation between the jump in temperature across a propagating phase boundary and the stability of solid phases. J. Elasticity, 13(4):357-378, 1983.

[26]

David Kinderlehrer, Richard James, Mitchell Luskin, and Jerry L. Ericksen, editors. Microstructure and phase transition. Springer-Verlag, New York, 1993.

[27]

D.J. Korteweg. Sur la forme que prennent les équations des mouvements des fluides si l'on tient compte des forces capillaires par des variations de densité. Arch. Néer. Sci. Exactes Sér. II, 6:1-24, 1901.

[28]

J. Lowengrub and L. Truskinovsky. Quasi-incompressible Cahn-Hilliard fluids and topological transitions. R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci., 454(1978):2617-2654, 1998.

[29]

Shing-Chung Ngan and Lev Truskinovsky. Thermal trapping and kinetics of martensitic phase boundaries. J. Mech. Phys. Solids, 47(1):141-172, 1999.

[30]

Robert L. Pego. Phase transitions in one-dimensional nonlinear viscoelasticity: admissibility and stability. Arch. Rational Mech. Anal., 97(4):353-394, 1987.

[31]

A. Pettinger and R. Abeyaratne. On the nucleation and propagation of thermoelastic phase transformations in anti-plane shear. I: Couple-stress theory. II: Problems. Comput. Mech., 26(1):13-38, 2000.

[32]

M. Rascle, D. Serre, and M. Slemrod, editors. PDEs and continuum models of phase transition, Berlin, 1989. Springer-Verlag.

[33]

J. S. Rowlinson. Translation of J. D. van der Waals' ``The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density''. J. Statist. Phys., 20(2):197-244, 1979.

[34]

J. S. Rowlinson and B. Widom. Molecular theory of capillarity. Oxford University Press, 1982.

[35]

D. Serre. Sur le principe variationnel des équations de la mécanique des fluides parfaits. RAIRO Modél. Math. Anal. Numér., 27(6):739-758, 1993.

[36]

Michael Shearer. Phase jumps near the Maxwell line. In Nonstrictly hyperbolic conservation laws (Anaheim, Calif., 1985), pages 111-114. Amer. Math. Soc., Providence, RI, 1987.

[37]

Michael Shearer. Dynamic phase transitions in a van der Waals gas. Quart. Appl. Math., 46(4):631-636, 1988.

[38]

M. Slemrod. Admissibility criteria for propagating phase boundaries in a van der Waals fluid. Arch. Rational Mech. Anal., 81(4):301-315, 1983.

[39]

M. Slemrod. Dynamic phase transitions in a van der Waals fluid. J. Differential Equations, 52(1):1-23, 1984.

[40]

Philip A. Thompson, Garry C. Carofano, and Yoon-Gong Kim. Shock waves and phase changes in a large-heat-capacity fluid emerging from a tube. J. Fluid Mech., 166:57-92, 1986.

[41]

C. Truesdell and W. Noll. The nonlinear field theories of mechanics. Springer-Verlag, Berlin, second edition, 1992.

[42]

L. Truskinovsky. Kinks versus shocks. In Shock induced transitions and phase structures in general media, pages 185-229. Springer, New York, 1993.

[43]

L. Truskinovsky. About the ``normal growth'' approximation in the dynamical theory of phase transitions. Contin. Mech. Thermodyn., 6(3):185-208, 1994.

[44]

M. Verschueren, F.N. van de Vosse, and H.E.H. Meijer. Diffuse-interface modelling of thermocapillary flow instabilities in a Hele-Shaw cell. J. Fluid Mech., 434:153-166, 2001.

[45]

Kevin Zumbrun. Dynamical stability of phase transitions in the p-system with viscosity-capillarity. SIAM J. Appl. Math., 60(6):1913-1924 (electronic), 2000.