Global solutions of a high dimensional system for Korteweg materials

Journal of Mathematical Analysis and Applications

Volumn 198, Issue 1, 1996, Pages 84-97

  Hattori, H H Harumi ^a   Li, Dening ^a  

^a WEST VIRGINIA UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030584308     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1996.0069     Document Type: Article

References (13)

1. 1. G. Andrews and J. M. Ball, Asymptotic behavior and change of phase in one-dimensional nonlinear viscoelasticity, J. Differential Equations 44 (1982), 306-341.
2. 2. J. E. Dunn and J. Serrin, On the thermodynamics of interstitial working, Arch. Rational Mech. Anal. 88 (1985), 95-133.
3. 3. H. Hattori and D. Li, Solutions for two dimensional system for materials of Korteweg type, SIAM J. Math. Anal. 25 (1994), 85-98.
4. 4. H. Hattori and K. Mischaikow, A dynamical systems approach to a phase transition problem, J. Differential Equations 94 (1991), 340-378.
5. 5. D. J. Korteweg, Sur la forme que prennent les équations des movement des fluides si l'on tient comple des forces capillaires par des variations de densité, Arch. Nederl. Sci. Exactes. Nat. Ser. II 6 (1901), 1-24.
6. 6. J. L. Lions and E. Magenes, "Nonhomogeneous Boundary Value Problems and Applications I," Springer-Verlag, New York, 1972.
7. 7. A. Matsumura and T. Nishida, The initial value problem for the equations of motion of viscous and heat-conductive gases, J. Math. Kyoto Univ. 20 (1980), 67-104.
8. 8. L. Nirenberg, On elliptic partial differential equations, Ann. Scuol. Norm. Sup. Pisa 13 (1959), 116-162.
9. 9. J. Serrin, The form of interfacial surfaces in Korteweg's theory of phase equilibria, Quart. J. Appl. Math. 41 (1983), 357-364.
10. 10. J. Serrin, Phase transition and interfacial layers for van der Waals fluids, in "Proceedings of SAFA IV Conference, Recent Methods in Nonlinear Analysis and Applications, Naples, 1980" (A. Camfora, S. Rionero, C. Sbordone, and C. Trombetti, Eds.).
11. 11. M. Slemrod, Admissibility criteria for propagating phase boundaries in a van der Waals fluid, Arch. Rational Mech. Anal. 81 (1983), 301-315.
12. 12. M. Slemrod, Dynamic phase transitions in a van der Waals fluid, J. Differential Equations 52 (1984), 1-23.
13. 13. J. Sprekels and S. Zheng, Global solutions to the equations of a Ginsburg-Landau theory for structural phase transitions in shape memory alloys, Physica D 39 (1989), 59-76.