Shadowing matching errors for wave-front-like solutions

Journal of Differential Equations

Volumn 129, Issue 2, 1996, Pages 403-457

  Lin, Xiao Biao ^a  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030578642     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1996.0123     Document Type: Article

References (32)

1. 1. N. Alikakos, P. Bates, and G. Fusco, Slow motion for the Cahn-Hilliard equation in one space dimension, J. Differential Equations 90 (1991), 81-135.
2. 2. S. B. Angenent, J. Mallet-Paret, and L. A. Peletier, Stable transition layers in a semilinear boundary value problem, J. Differential Equations 67 (1987), 212-242.
3. 3. P. Bates and P. J. Xun, Metastable Patterns for the Cahn-Hilliard Equation: Part I and II, preprint.
4. 4. M. S. Berger and L. E. Fraenkel, On singular perturbations of nonlinear operator equations, Indiana Univ. Math. J. 20 (1971), 623-631.
5. xx - f(u), Comm. Pure Appl. Math. 42 (1989), 523-576.
6. 6. W. A. Coppel, Dichotomies in stability theory, in "Lecture Notes in Math." (A. Dold and B. Eckmann, Eds.), Vol. 629, Springer-Verlag, New York, 1970.
7. 7. W. Eckhaus, Matching principles and composite expansions, in "Lecture Notes in Mathematics," Vol. 594, pp. 146-147, Springer-Verlag, New York, 1977.
8. 8. W. Eckhaus, "Asymptotic Analysis of Singular Perturbations," North-Holland, Amsterdam, 1979.
9. 9. John W. Evans, Nerve axon equations: I Linear approximations, Indiana Univ. Math. J. 21 (1972), 877-885.
10. 10. John W. Evans, Nerve axon equations: II Stability at rest, Indiana Univ. Math. J. 22 (1972), 75-90.
11. 11. John W. Evans, Nerve axon equations: III Stability of the nerve impulse, Indiana Univ. Math. J. 22 (1972), 577-593.
12. 12. John W. Evans, Nerve axon equations: IV The stable and the unstable impulse, Indiana Univ. Math. J. 24 (1975), 1169-1190.
13. 13. P. C. Fife, Pattern formation in reacting and diffusing systems, J. Chem. Phys. 64 (1976), 554-564.
14. 14. P. C. Fife, Singular perturbation and wave front techniques in reaction-diffusion problems, SIAM-AMS Proc. 10 (1976), 23-50.
15. 15. P. C. Fife, Dynamics of internal layers and diffusive interfaces, CBMS-NSF, Reg. Conf. Ser. Appl. Math., SIAM 1988.
16. 16. P. C. Fife, Diffusive waves in inhomogeneous media, Proc. Edinburgh Math. Soc. 32 (1989), 291-315.
17. 17. P. C. Fife and L. Hsiao, The generation of solutions of internal layers, J. Nonlinear Anal. TMA 12 (1988), 19-41.
18. 18. G. Fusco and J. Hale, Slow motion manifolds, dormant instability, and singular perturbations, J. Dynamics Differential Equations 1 (1989), 75-94.
19. 19. R. A. Gardner and C. K. R. T. Jones, Traveling waves of a perturbed diffusion equation arising in a phase field model, Indiana Univ. Math. J. 38 (1989), 1197-1222.
20. 20. J. K. Hale and K. Sakamoto, Existence and stability of transition layers, Jpn. J. Appl. Math. 5 (1988), 367-405.
21. 21. K. Kirchgässner, Homoclinic bifurcation of perturbed reversible systems, in "Lecture Notes in Math." (W. Knobloch and K. Smith, Eds.), Vol. 1017, pp. 328-363, Springer-Verlag, New York, 1982.
22. 22. C. Jones and N. Kopell, Tracking invariant manifolds with differential forms in singularly perturbed systems, J. Differential Equations 108 (1994), 64-89.
23. 23. X.-B. Lin, Shadowing lemma and singularly perturbed boundary value problems, SIAM J. Appl. Math. 49 (1989), 26-54.
24. 24. X.-B. Lin, Heteroclinic bifurcation and singularly perturbed boundary value problems, J. Differential Equations 84 (1990), 319-382.
25. 25. X.-B. Lin, Asymptotic expansion for layer solutions of a singularly perturbed reaction-diffusion system, Trans. Amer. Math. Soc. 348 (1996), 713-753.
26. 26. X.-B. Lin, Exponential dichotomies in intermediate spaces with applications to a diffusively perturbed predator-prey model, J. Differential Equations 108 (1994), 36-63.
27. 27. X.-B. Lin, Local and global existence of multiple waves near formal approximations, Progr. Nonlinear Differential Equations Appl. 19 (1996), 385-404.
28. 28. J. L. Lions and E. Magenes, "Non-Homogeneous Boundary Value Problems and Applications I," Springer-Verlag, New York, 1972.
29. 29. K. J. Palmer, Exponential dichotomies and transversal homoclinic points, J. Differential Equations 55 (1984), 225-256.
30. 30. M. Renardy, Bifurcation of singular solutions in reversible systems and applications to reaction-diffusion equations, Adv. Math. 3 (1982), 324-406.
31. 31. A. Pazy, "Semigroups of Linear Operators and Applications to Partial Differential Equations," Springer, New York, 1983.
32. 32. K. Yosida, "Functional Analysis," Grundlehren der mathematischen Wissenschaften 123, Springer, New York, 1980.