This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
J. D. van der Waals, The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density (in Dutch), Verh. Konink. Acad. Wetensch., Amsterdam (Sec 1), Vol. No. 8 (1893).
J. W. Cahn and J. E. Hilliard, Free energy of a nonuniform system, I: Interfacial free energy. J. Chem. Phys., 28, 258–267 (1958).
M. Slemrod, Admissibility criteria for propagating phase boundaries in a van der Waals fluid, Arch. Rational Mech. Anal., 81, 301–315 (1983).
M. Shearer, The Riemann problem for a clas of conservation laws of mixed type, J. Differential Equations, 46, 426–443 (1982).
M. Shearer, Nonuniqueness of admissible solutions of the Riemann initial value problem for a system of conservation laws of mixed type, Arch. Rational Mech. Anal., 93, 45–59 (1986).
R. Hagan and M. Slemrod, The viscosity-capillarity criterion for shocks and phas transitions, Arch. Rational Mech. Anal., 83, 333–361 (1984).
M. Grinfeld, Topological techniques in the dynamics of phas transitions, Ph.D. Thesis, Rensselaer Polytechnic Institute (1986).
R. Hagan and J. Serrin, One dimensional shock layers in Korteweg fluids, in Phase Transformations and Material Instabilities, ed. M. E. Gurtin, Academic Press, New York (1984).
M. Shearer, Riemann problem for a van der Waals fluid, to appear Quarterly of Applied Mathematics.
R. Pego, Phase transitions. in one dimensional nonlinear viscoelasticity: Admissibility and stability, Arch. Rational Mech. Anal., 353–394 (1987).
G. Andrews and J. M. Ball, Asymptotic behavior of changes of phase in one dimensional nonlinear viscoelasticity, J. Differential Equations 6, 71–86 (1982).
G. Maugin, Continuum Mechanics of Electro-magnetic Solids, North-Holland (Amsterdam), 1988.
M. Slemrod, A limiting “viscosity” approach to the Riemann problem for materials exhibiting change of phase, to appear Arch. Rational Mech. Anal.
A. S. Kalasnikov, Construction of generalized solutions of quasilinear equations of first order without convexity conditions as limits of solutions of parabolic equations with a small parameter, Dokl. Akad. Nauk SSR 127, 27–30 (1959) (Russian).
V. A. Tupciev, The asymptotic behavior of solution of the Cauchy problem for the equation ε2tuxx = ut + [ϕ(u)]x that degenerates for ξ = 0 into the problem of the decay of an arbitrary discontinuity for the case of a rare faction wave. Zh. Vychisl. Mat. i Fiz. 12, 770–775 (1972). English translation in USSR, Comput. Math. and Phys. 12.
C. M. Dafermos, Solution of the Riemann problem for a class of hyperbolic systems of conservation laws by the viscosity method, Arch. Rational Mech. Anal., 52, 1–9 (1973).
C. M. Dafermos, Structure of solutions of the Riemann problem for hyperbolic systems of conservation laws, Arch. Rational Mech. Anal., 53, 203–217 (1974).
C. M. Dafermos and R. DiPerna, The Riemann problem for certain classes of hyperbolic systems of conservation laws, J. Differential Equations, 90–114 (1976).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1989 Springer-Verlag
About this paper
Cite this paper
Slemrod, M. (1989). The viscosity-capillarity approach to phase transitions. In: Rascle, M., Serre, D., Slemrod, M. (eds) PDEs and Continuum Models of Phase Transitions. Lecture Notes in Physics, vol 344. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0024944
Download citation
DOI: https://doi.org/10.1007/BFb0024944
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-51617-0
Online ISBN: 978-3-540-46717-5
eBook Packages: Springer Book Archive