This is a preview of subscription content, log in via an institution to check access.
References
[1893] van der Waals, J. D., The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density (in Dutch), Verhandel. Konink. Akad. Weten. Amsterdam (Sec. 1) Vol. 1, No. 8.
[1958] Cahn, J. W., & J. E. Hilliard, Free energy of a nonuniform system. I. Interfacial free energy, J. Chem. Physics 28, 258–267.
[1962] Toupin, R. A., Elastic materials with couple-stresses, Arch. Rational Mech. Anal. 11, 385–414.
[1966] Morrey, C. B., Multiple Integrals in the Calculus of Variations, Springer-Verlag, Berlin Heidelberg New York.
[1969] Hale, J. K., Ordinary Differential Equations, Wiley Interscience, New York.
[1971] Langer, J. S., Theory of spinodal decomposition in alloys, Ann. Phys. 65, 53–87.
[1973] Antman, S. S., Nonuniqueness of equilibrium states for bars in tension, J. Math. Anal. Appl. 44, 333–349.
[1974] Antman, S. S., Qualitative theory of the ordinary differential equations of nonlinear elasticity, Mechanics Today, 1972; Pergamon, New York, 58–101.
[1975] Ericksen, J. L., Equilibrium of bars, J. Elasticity 5, 191–201.
[1977] Antman, S. S., & E. R. Carbone, Shear and necking instabilities in nonlinear elasticity, J. Elast. 7, 125–151.
[1977] Jackiw, R., Quantum meaning of classical field theory, Rev. Modern Phys. 49, 681–706.
[1978] Arnold, V., Mathematical Methods of Classical Mechanics, Springer-Verlag, Berlin Heidelberg New York.
[1979] Rowlinson, J. S., Translation of J. D. van der Waals “The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density”, J. Stat. Phys. 20, 197–244.
[1982] Davis, H. T., & L. E. Scriven, Stress and structure in fluid interfaces, Advances Chem. Phys. 49, 681–706.
[1983] Aifantis, E. C. & J. B. Serrin, The mechanical theory of fluid interfaces and Maxwell's rule, J. Colloidal Interface Sci. 96, 517–529.
[1983] Aifantis, E. C. & J. B. Serrin, Equilibrium solutions in the mechanical theory of fluid microstuctures, J. Colloidal Interface Sci. 96, 530–547.
[1983] Carr, J., M. E. Gurtin, & M. Slemrod, One-dimensional structured phase transformations under prescribed loads, Technical Report 2559, Mathematics Research Center, University of Wisconsin, Madison. To appear in J. Elast.
[1983] Coleman, B. D., Necking and drawing in polymeric fibers under tension, Arch. Rational Mech. Anal. 83, 115–137.
[1984] Novick-Cohen, A., & L. A. Segel, Nonlinear aspects of the Cahn-Hilliard equation, Physica 10D, 277–298.
[1984] Novick-Cohen, A., The nonlinear Cahn-Hilliard equation: Transition from spinodal decomposition to nucleation behavior. To appear.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Carr, J., Gurtin, M.E. & Slemrod, M. Structured phase transitions on a finite interval. Arch. Rational Mech. Anal. 86, 317–351 (1984). https://doi.org/10.1007/BF00280031
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00280031