메뉴 건너뛰기




Volumn 348, Issue 2, 1996, Pages 713-753

Asymptotic expansion for layer solutions of a singularly perturbed reaction-diffusion system

Author keywords

Asymptotic expansions; Boundary internal and initial layers; Reaction diffusion systems; Singular perturbations; Stability

Indexed keywords


EID: 21344472255     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-96-01542-5     Document Type: Article
Times cited : (8)

References (31)
  • 1
    • 44949275928 scopus 로고
    • Slow motion for the Cahn-Hilliard equation in one space dimension
    • MR 92a:35152
    • 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. MR 92a:35152
    • (1991) J. Differential Equations , vol.90 , pp. 81-135
    • Alikakos, N.1    Bates, P.2    Fusco, G.3
  • 2
    • 0000005962 scopus 로고
    • Stable transition layers in a semilinear boundary value problem
    • MR 88d:34018
    • 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. MR 88d:34018
    • (1987) J. Differential Equations , vol.67 , pp. 212-242
    • Angenent, S.B.1    Mallet-Paret, J.2    Peletier, L.A.3
  • 4
    • 85025784004 scopus 로고
    • An example of bifurcation to homoclinic orbits
    • MR 81m:58056
    • S.-N. Chow, J. Hale and J. Mallet-Paret, An example of bifurcation to homoclinic orbits, J. Differential Equations, 37 (1980), 351-373. MR 81m:58056
    • (1980) J. Differential Equations , vol.37 , pp. 351-373
    • Chow, S.-N.1    Hale, J.2    Mallet-Paret, J.3
  • 5
    • 0002500168 scopus 로고
    • Equations d'evolution abstraites non linéaires de type parabolique
    • MR 81d:34052
    • G. Da Prato and P. Grisvard, Equations d'evolution abstraites non linéaires de type parabolique, Ann. Mat. Pura. Appl., 120 (1979), 329-396. MR 81d:34052
    • (1979) Ann. Mat. Pura. Appl. , vol.120 , pp. 329-396
    • Da Prato, G.1    Grisvard, P.2
  • 6
    • 0009086759 scopus 로고
    • Matching principles and composite expansions
    • Springer-Verlag, New York, MR 58:6857
    • W. Eckhaus, Matching principles and composite expansions, Lecture Notes in Mathematics 594, Springer-Verlag, New York, 1977, 146-177. MR 58:6857
    • (1977) Lecture Notes in Mathematics , vol.594 , pp. 146-177
    • Eckhaus, W.1
  • 8
    • 0001472248 scopus 로고
    • Nerve Axon Equations: I Linear Approximations
    • MR 45:1616
    • John W. Evans, Nerve Axon Equations: I Linear Approximations, Indiana Univ. Math. J., 21 (1972), 877-885. MR 45:1616
    • (1972) Indiana Univ. Math. J. , vol.21 , pp. 877-885
    • Evans, J.W.1
  • 9
    • 0001472247 scopus 로고
    • Nerve Axon Equations: II Stability at Rest
    • MR 48:1729
    • John W. Evans, Nerve Axon Equations: II Stability at Rest, Indiana Univ. Math. J., 22 (1972), 75-90. MR 48:1729
    • (1972) Indiana Univ. Math. J. , vol.22 , pp. 75-90
    • Evans, J.W.1
  • 10
    • 0001472246 scopus 로고
    • Nerve Axon Equations: III Stability of the Nerve Impulse
    • MR 52:14697
    • John W. Evans, Nerve Axon Equations: III Stability of the Nerve Impulse, Indiana Univ. Math. J.; 22 (1972), 577-593. MR 52:14697
    • (1972) Indiana Univ. Math. J. , vol.22 , pp. 577-593
    • Evans, J.W.1
  • 11
    • 0016578299 scopus 로고
    • Nerve Axon Equations: IV the Stable and the Unstable Impulse
    • MR 52:14698
    • John W. Evans, Nerve Axon Equations: IV The Stable and the Unstable Impulse, Indiana Univ. Math. J., 24 (1975), 1169-1190. MR 52:14698
    • (1975) Indiana Univ. Math. J. , vol.24 , pp. 1169-1190
    • Evans, J.W.1
  • 12
    • 0000253608 scopus 로고
    • Pattern formation in reacting and diffusing systems
    • P. C. Fife, Pattern formation in reacting and diffusing systems, J. Chem. Phys., 64 (1976), 554-564.
    • (1976) J. Chem. Phys. , vol.64 , pp. 554-564
    • Fife, P.C.1
  • 13
    • 0011653786 scopus 로고
    • Singular perturbation and wave front techniques in reaction-diffusion problems
    • MR 58:25358
    • P. C. Fife, Singular perturbation and wave front techniques in reaction-diffusion problems, SIAM-AMS Proceedings, 10 (1976),23-50. MR 58:25358
    • (1976) SIAM-AMS Proceedings , vol.10 , pp. 23-50
    • Fife, P.C.1
  • 15
    • 84975973968 scopus 로고
    • Diffusive waves in inhomogeneous media
    • MR 90j:35109
    • P. C. Fife, Diffusive waves in inhomogeneous media, Proc. Edinburgh Math. Soc., 32 (1989), 291-315. MR 90j:35109
    • (1989) Proc. Edinburgh Math. Soc. , vol.32 , pp. 291-315
    • Fife, P.C.1
  • 16
    • 0002626726 scopus 로고
    • The generation of solutions of internal layers
    • MR 89c:35078
    • P. C. Fife and L. Hsiao, The generation of solutions of internal layers, J. Nonlinear Anal. TMA 12 (1988), 19-41. MR 89c:35078
    • (1988) J. Nonlinear Anal. TMA , vol.12 , pp. 19-41
    • Fife, P.C.1    Hsiao, L.2
  • 17
    • 0001863910 scopus 로고
    • Slow motion manifolds, dormant instability, and singular perturbations
    • MR 90i:35131
    • G. Fusco and J. Hale, Slow motion manifolds, dormant instability, and singular perturbations, J. Dynamics and Differential Equations 1 (1989), 75-94. MR 90i:35131
    • (1989) J. Dynamics and Differential Equations , vol.1 , pp. 75-94
    • Fusco, G.1    Hale, J.2
  • 18
    • 0001330437 scopus 로고
    • Heteroclinic orbits for retarded functional differential equations
    • MR 88g:34113
    • J. K. Hale and X.-B. Lin, Heteroclinic orbits for retarded functional differential equations, J. Differential Equations 65 (1986), 175-202. MR 88g:34113
    • (1986) J. Differential Equations , vol.65 , pp. 175-202
    • Hale, J.K.1    Lin, X.-B.2
  • 19
    • 0000446574 scopus 로고
    • Existence and stability of transition layers
    • MR 90a:35112
    • J. K. Hale and K. Sakamoto, Existence and stability of transition layers, Japan Journal of Appl. Math. 5 (1988), 367-405. MR 90a:35112
    • (1988) Japan Journal of Appl. Math. , vol.5 , pp. 367-405
    • Hale, J.K.1    Sakamoto, K.2
  • 20
    • 84967743294 scopus 로고
    • Stability of the travelling wave solution, of the FizHugh-Nagumo system
    • MR 86b:35011
    • C. Jones, Stability of the travelling wave solution, of the FizHugh-Nagumo system, Trans. Amer. Math. Soc. 286 (1984), 431-469. MR 86b:35011
    • (1984) Trans. Amer. Math. Soc. , vol.286 , pp. 431-469
    • Jones, C.1
  • 21
    • 0002809936 scopus 로고
    • Tracking invariant manifolds with differential forms in singularly perturbed systems
    • C. Jones and N. Kopell, Tracking invariant manifolds with differential forms in singularly perturbed systems, J. Differential Equations, 108 (1994), 64-88.
    • (1994) J. Differential Equations , vol.108 , pp. 64-88
    • Jones, C.1    Kopell, N.2
  • 22
    • 0002861754 scopus 로고
    • Shadowing lemma and singularly perturbed boundary value problems
    • MR 90a:34126
    • X.-B. Lin, Shadowing lemma and singularly perturbed boundary value problems, SIAM J. Appl. Math., 40 (1989), 26-54. MR 90a:34126
    • (1989) SIAM J. Appl. Math. , vol.40 , pp. 26-54
    • Lin, X.-B.1
  • 23
    • 38249018789 scopus 로고
    • Heteroclinic bifurcation and singularly perturbed boundary value problems
    • MR 91d:34055
    • X.-B. Lin, Heteroclinic bifurcation and singularly perturbed boundary value problems, J. Differential Equations, 84 (1990), 319-382. MR 91d:34055
    • (1990) J. Differential Equations , vol.84 , pp. 319-382
    • Lin, X.-B.1
  • 24
    • 51249176356 scopus 로고
    • On the evolution operator for abstract parabolic equations
    • MR 89f:47066
    • A. Lunardi, On the evolution operator for abstract parabolic equations, Israel J. Math., 60 (1987), 281-314. MR 89f:47066
    • (1987) Israel J. Math. , vol.60 , pp. 281-314
    • Lunardi, A.1
  • 25
    • 0000988067 scopus 로고
    • Stability of singularly perturbed solutions to systems of reactiondiffusion equations
    • MR 88j:35089
    • Y. Nishiura and H. Fujii, Stability of singularly perturbed solutions to systems of reactiondiffusion equations, SIAM J. Math. Anal. 18 (1987), 1726-1770. MR 88j:35089
    • (1987) SIAM J. Math. Anal. , vol.18 , pp. 1726-1770
    • Nishiura, Y.1    Fujii, H.2
  • 26
    • 48549112859 scopus 로고
    • Exponential dichotomies and transversal homoclinic points
    • MR 86d:58088
    • K. J. Palmer, Exponential dichotomies and transversal homoclinic points, J. Differential Equations 55 (1984), 225-256. MR 86d:58088
    • (1984) J. Differential Equations , vol.55 , pp. 225-256
    • Palmer, K.J.1
  • 28
    • 0000814275 scopus 로고
    • On the stability of travelling waves
    • MR 55:8561
    • D. Sattinger, On the stability of travelling waves, Adv. Math., 22 (1976), 312-335. MR 55:8561
    • (1976) Adv. Math. , vol.22 , pp. 312-335
    • Sattinger, D.1
  • 29
    • 0039685238 scopus 로고
    • Weighted norms for the stability of travelling waves
    • MR 56:6123
    • D. Sattinger, Weighted norms for the stability of travelling waves, J. Differential Equations, 25 (1977), 130-144. MR 56:6123
    • (1977) J. Differential Equations , vol.25 , pp. 130-144
    • Sattinger, D.1
  • 31
    • 0002461654 scopus 로고
    • On the abstract Cauchy problem of parabolic type in spaces of continuous functions
    • MR 86g:34086
    • E. Sinestrari, On the abstract Cauchy problem of parabolic type in spaces of continuous functions, J. Math. Anal. Appl., 107 (1985), 16-66. MR 86g:34086
    • (1985) J. Math. Anal. Appl. , vol.107 , pp. 16-66
    • Sinestrari, E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.