Transition layer solutions of a higher order equation in an infinite tube

Communications in Partial Differential Equations

Volumn 21, Issue 1-2, 1996, Pages 109-145

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

^a BRIGHAM YOUNG UNIVERSITY   (United States)

^b UNIVERSITY OF MINNESOTA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0013197527     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: 10.1080/03605309608821180     Document Type: Article

References (11)

1. R.A. Adams, Sobolev Spaces, Academic Press, New York, 1975.
2. P.W. Bates, P.C. Fife, R. Gardner and C.K.R.T. Jones, Phase field models for hypercooled solidification, preprint.
3. P.W. Bates, P.C. Fife, R. Gardner and C.K.R.T. Jones, The existence of traveling wave solutions of a generalized phase-field model, preprint.
4. P.W. Bates, P.C. Fife, X. Ren and X. Wang, Traveling waves in a convolution model for phase transitions, preprint.
5. P.W. Bates and X. Ren. Heteroclinic orbits for a higher order phase transition problem, preprint.
6. P. Fife and J.B. McLeod. The approach of solutions of nonlinear diffusion equations to traveling front solutions, Arch. Rat. Mech. Anal. 65 (1977), 335-361.
7. R. Gardner and C.K.R.T. Jones, Traveling waves of a perturbed diffusion equation arising in a phase field model, Indiana Math. J. Vol 38, no. 4 (1989), 1197-1222.
8. A.G. Khachaturyan, 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, Vol. 9 (1968), 2040-2046.
9. A.G. Khachaturyan, Theory of Structural Transformations in Solids, Wiley-Interscience Publications, New York, 1983.
10. P.L. Lions. 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. (1984). 109-145, 223-283.
11. X. Ren, Variational approach to multiple layers of the bistable equation in long tubes, preprint.