Heteroclinic orbits for a higher order phase transition problem

European Journal of Applied Mathematics

Volumn 8, Issue 2, 1997, Pages 149-163

  Bates, Peter W ^b   Ren, Xiaofeng ^a,b  

^a UTAH STATE UNIVERSITY   (United States)

^b BRIGHAM YOUNG UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031478385     PISSN: 09567925     EISSN: None     Source Type: Journal    
DOI: 10.1017/s0956792597002994     Document Type: Article

References (17)

1. KHACHATURYAN, A. G. (1968) Microscopic theory of diffusion in crystalline solid solutions and the time evolution of the diffuse scattering of X rays and thermal neutrons. Soviet Phys. Solid State, 9, 2040-2046.
2. KHACHATURYAN, A. G. (1983) Theory of Structural Transformations in Solids. Wiley-Interscience.
3. BRAGG, W. L. & WILLIAMS, E. J. (1934) Effect of thermal agitation on atomic arrangement in alloys. Proc. Roy. Soc. London Ser. A, 145, 699-730.
4. HAASEN, P. (1978) Physical Metallurgy. Cambridge University Press.
5. BELLETINI, G. & PRESUTTI, E. In preparation.
6. LEBOWITZ, J. L. & PENROSE, O. (1966) Rigorous treatment of the van der Waals-Maxwell theory of liquid-vapor transition. J. Math. Phys. 7, 98-113.
7. DEMASI, A., ORLANDI, E., PRESUTTI, E. & TRIOLO, L. (1994) Glauber evolution with Kac potentials: I. Mesoscopic and macroscopic limits, interface dynamics. Nonlinearity, 7, 633-696.
8. KATSOULAKIS, M. & SOUGANIDIS, P. E. (1994) Interacting particle systems and generalized front propagation. Arch. Rat. Mech. Anal., 127, 133-157.
9. SOUGANIDIS, P. E. (1997) Interface dynamics in phase transitions. Proceedings of the 1994 ICM. To appear.
10. BATES, P. W., FIFE, P. C., REN, X. & WANG, X. (1997) Traveling waves in a convolution model for phase transitions. Arch. Rat. Mech. Anal. To appear.
11. BATES, P. W., FIFE, P. C., GARDNER, R. & JONES, C. K. R. T. (1977) Phase field models for hypercooled solidification. Physica. To appear.
12. BATES, P. W. & REN, X. (1996) Transition layer solutions of a higher order equation in an infinite tube. Comm. Partial Differential Equations, 21, 195-220.
13. FIFE, P. & MCLEOD, J. B. (1977) The approach of solutions of nonlinear diffusion equations to traveling front solutions. Arch. Rat. Mech. Anal., 65, 335-361.
14. GARDNER, R. & JONES, C. K. R. T. (1989) Traveling waves of a perturbed diffusion equation arising in a phase field model. Indiana Math. J., 38 (4), 1197-1222.
15. BATES, P. W., FIFE, P. C., GARDNER, R. & JONES, C. K. R. T. (1977) The existence of traveling wave solutions of a generalized phase-field model. SIAM J. Math. Anal. 28 (1), 60-93.
16. LIONS, P. L. (1984) The concentration-compactness principle in the calculus of variations: The locally compact case. Part I and Part II. Ann. Inset. H. Poincare Sect. A (N.S.) 1, 109-145, 223-283.
17. ADAMS, R. A. (1975) Sobolev Spaces, Academic Press.