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Volumn 154, Issue 2, 1999, Pages 364-418

Multiple internal layer solutions generated by spatially oscillatory perturbations

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EID: 0033586857     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1998.3566     Document Type: Article
Times cited : (12)

References (35)
  • 2
    • 0002317927 scopus 로고    scopus 로고
    • S-Shaped bifurcation of a singularly perturbed boundary value problem
    • Brunovský P. S-Shaped bifurcation of a singularly perturbed boundary value problem. J. Differential Equations. 145:1998;52-100.
    • (1998) J. Differential Equations , vol.145 , pp. 52-100
    • Brunovský, P.1
  • 3
    • 0028045155 scopus 로고
    • Explanation of spurt for a non-Newtonian fluid by a diffusion term
    • Brunovský P., Sevcovic D. Explanation of spurt for a non-Newtonian fluid by a diffusion term. Quart. Appl. Math. 52:1994;401-426.
    • (1994) Quart. Appl. Math. , vol.52 , pp. 401-426
    • Brunovský, P.1    Sevcovic, D.2
  • 6
    • 0003805267 scopus 로고
    • Lecture Notes in Mathematics. Berlin: Springer-Verlag
    • Coppel W. A. Dichotomies in Stability Theory. Lecture Notes in Mathematics. 629:1978;Springer-Verlag, Berlin.
    • (1978) Dichotomies in Stability Theory , vol.629
    • Coppel, W.A.1
  • 7
    • 34250627892 scopus 로고
    • Geometric singular perturbation theory for differential equations
    • Fenichel N. Geometric singular perturbation theory for differential equations. J. Differential Equations. 31:1979;53-98.
    • (1979) J. Differential Equations , vol.31 , pp. 53-98
    • Fenichel, N.1
  • 8
    • 0016950595 scopus 로고
    • Boundary and interior transition layer phenomena for pairs of second-order differential equations
    • Fife P. C. Boundary and interior transition layer phenomena for pairs of second-order differential equations. J. Math. Anal. Appl. 54:1976;497-521.
    • (1976) J. Math. Anal. Appl. , vol.54 , pp. 497-521
    • Fife, P.C.1
  • 9
    • 0002626726 scopus 로고
    • The generating of solutions of internal layers
    • Fife P. C., Hsiao L. The generating of solutions of internal layers. Nonlinear Anal. 12:1988;19-41.
    • (1988) Nonlinear Anal. , vol.12 , pp. 19-41
    • Fife, P.C.1    Hsiao, L.2
  • 10
    • 0009033558 scopus 로고
    • Neumann layer phenomena in nonlinear diffusion systems
    • Fujii H., Hosono Y. Neumann layer phenomena in nonlinear diffusion systems. Lecture Notes Numer. Appl. Anal. 6:1983;21-38.
    • (1983) Lecture Notes Numer. Appl. Anal. , vol.6 , pp. 21-38
    • Fujii, H.1    Hosono, Y.2
  • 11
    • 0001863910 scopus 로고
    • Slow motion manifolds, dormant instability, and singular perturbations
    • Fusco G., Hale J. Slow motion manifolds, dormant instability, and singular perturbations. J. Dynam. Differential Equations. 1:1989;75-94.
    • (1989) J. Dynam. Differential Equations , vol.1 , pp. 75-94
    • Fusco, G.1    Hale, J.2
  • 13
    • 0000446574 scopus 로고
    • Existence and stability of transition layers
    • Hale J., Sakamoto K. Existence and stability of transition layers. Japan J. Appl. Math. 5:1988;367-405.
    • (1988) Japan J. Appl. Math. , vol.5 , pp. 367-405
    • Hale, J.1    Sakamoto, K.2
  • 14
    • 0000167408 scopus 로고
    • Singular perturbation approach to traveling waves in competing and diffusing species models
    • Hosono Y., Mimura M. Singular perturbation approach to traveling waves in competing and diffusing species models. J. Math. Kyoto Univ. 22/23:1982;435-461.
    • (1982) J. Math. Kyoto Univ. , vol.2223 , pp. 435-461
    • Hosono, Y.1    Mimura, M.2
  • 15
    • 0000653552 scopus 로고
    • Global bifurcation phenomena of travelling wave solutions for some bistable reaction-diffusion systems
    • Ikeda H., Mimura M., Nishiura Y. Global bifurcation phenomena of travelling wave solutions for some bistable reaction-diffusion systems. Nonlinear Anal. 13:1989;507-526.
    • (1989) Nonlinear Anal. , vol.13 , pp. 507-526
    • Ikeda, H.1    Mimura, M.2    Nishiura, Y.3
  • 16
    • 0002316532 scopus 로고
    • Geometric singular perturbation theory
    • Lecture Notes in Math. Berlin/New York: Springer-Verlag. p. 44-118
    • Jones C. K. R. T. Geometric singular perturbation theory. Dynamical Systems. Lecture Notes in Math. 1069:1995;Springer-Verlag, Berlin/New York. p. 44-118.
    • (1995) Dynamical Systems , vol.1069
    • Jones, C.K.R.T.1
  • 17
    • 0002809936 scopus 로고
    • Tracking invariant manifolds with differential forms in singularly perturbed systems
    • Jones C., Kopell N. Tracking invariant manifolds with differential forms in singularly perturbed systems. J. Differential Equations. 108:1994;64-89.
    • (1994) J. Differential Equations , vol.108 , pp. 64-89
    • Jones, C.1    Kopell, N.2
  • 18
    • 38249016389 scopus 로고
    • Heteroclinic and homoclinic bifurcation in bistable reaction diffusion systems
    • Kokubu H., Nishiura Y., Oka H. Heteroclinic and homoclinic bifurcation in bistable reaction diffusion systems. J. Differential Equations. 86:1990;260-341.
    • (1990) J. Differential Equations , vol.86 , pp. 260-341
    • Kokubu, H.1    Nishiura, Y.2    Oka, H.3
  • 20
    • 0002861754 scopus 로고
    • Shadowing lemmas and singularly perturbed boundary value problems
    • Lin X.-B. Shadowing lemmas and singularly perturbed boundary value problems. SIAM J. Appl. Math. 49:1989;26-54.
    • (1989) SIAM J. Appl. Math. , vol.49 , pp. 26-54
    • Lin, X.-B.1
  • 21
    • 38249018789 scopus 로고
    • Heteroclinic bifurcation and singularly pertrubed boundary value problems
    • Lin X.-B. Heteroclinic bifurcation and singularly pertrubed boundary value problems. J. Differential Equations. 84:1990;319-382.
    • (1990) J. Differential Equations , vol.84 , pp. 319-382
    • Lin, X.-B.1
  • 22
    • 84972438215 scopus 로고
    • Using melnikov's method to solve Silnikov's problems
    • Lin X.-B. Using melnikov's method to solve Silnikov's problems. Proc. Royal Soc. Edinburgh Sect. A. 116:1990;295-325.
    • (1990) Proc. Royal Soc. Edinburgh Sect. A , vol.116 , pp. 295-325
    • Lin, X.-B.1
  • 23
    • 0001405831 scopus 로고    scopus 로고
    • Local and global existence of multiple wave near formal approxiations
    • Cambridge: Birkhäuser Boston. p. 385-404
    • Lin X.-B. Local and global existence of multiple wave near formal approxiations. Prog. Nonlinear Differential Equations Appl. 1996;Birkhäuser Boston, Cambridge. p. 385-404.
    • (1996) Prog. Nonlinear Differential Equations Appl.
    • Lin, X.-B.1
  • 24
    • 21344472255 scopus 로고    scopus 로고
    • Asymptotic expansion for layer solutions of a singularly perturbed reaction-diffusion system
    • Lin X.-B. Asymptotic expansion for layer solutions of a singularly perturbed reaction-diffusion system. Trans. Am. Math. Soc. 348:1996;713-753.
    • (1996) Trans. Am. Math. Soc. , vol.348 , pp. 713-753
    • Lin, X.-B.1
  • 25
    • 0030578642 scopus 로고    scopus 로고
    • Shadowing matching errors for wave front like solutions
    • Lin X.-B. Shadowing matching errors for wave front like solutions. J. Differential Equations. 129:1996;403-457.
    • (1996) J. Differential Equations , vol.129 , pp. 403-457
    • Lin, X.-B.1
  • 27
    • 85009592686 scopus 로고
    • Asymptotic behavior and stability of solutions of semilinear diffusion equations
    • Matano H. Asymptotic behavior and stability of solutions of semilinear diffusion equations. Publ. Res. Inst. Math. Sci. 15:1979;401-458.
    • (1979) Publ. Res. Inst. Math. Sci. , vol.15 , pp. 401-458
    • Matano, H.1
  • 28
    • 0000082814 scopus 로고
    • Multiple solutions of two-point boundary value problems of Neumann type with a small parameter
    • Mimura M., Tabata M., Hosono Y. Multiple solutions of two-point boundary value problems of Neumann type with a small parameter. SIAM J. Math. Anal. 11:1980;613-631.
    • (1980) SIAM J. Math. Anal. , vol.11 , pp. 613-631
    • Mimura, M.1    Tabata, M.2    Hosono, Y.3
  • 29
    • 0002882425 scopus 로고
    • Coexistence of infinitely many stable solutions to reaction diffusion systems in the singular limit
    • Nishiura Y. Coexistence of infinitely many stable solutions to reaction diffusion systems in the singular limit. Dynamics Reported, New Series. 3:1994;25-103.
    • (1994) Dynamics Reported, New Series , vol.3 , pp. 25-103
    • Nishiura, Y.1
  • 30
    • 0000988067 scopus 로고
    • Stability of singularly perturbed solutions to systems of reaction-diffusion equations
    • Nishiura Y., Fujii H. Stability of singularly perturbed solutions to systems of reaction-diffusion equations. SIAM J. Math. Anal. 18:1987;1726-1770.
    • (1987) SIAM J. Math. Anal. , vol.18 , pp. 1726-1770
    • Nishiura, Y.1    Fujii, H.2
  • 31
    • 0008980441 scopus 로고
    • SLEP method to the stability of singularly pertrubed solutions with multiple transition layers in reaction-diffusion systems
    • J. Hale, & S.-N. Chow. Berlin/New York: Springer-Verlag
    • Nishiura Y., Fujii H. SLEP method to the stability of singularly pertrubed solutions with multiple transition layers in reaction-diffusion systems. Hale J., Chow S.-N., Dynamics of Infinite Dimensional Systems. 1987;Springer-Verlag, Berlin/New York.
    • (1987) Dynamics of Infinite Dimensional Systems
    • Nishiura, Y.1    Fujii, H.2
  • 32
    • 48549112859 scopus 로고
    • Exponential dichotomies and transversal homoclinic points
    • Palmer K. J. Exponential dichotomies and transversal homoclinic points. J. Differential Equations. 55:1984;225-256.
    • (1984) J. Differential Equations , vol.55 , pp. 225-256
    • Palmer, K.J.1
  • 33
    • 84972577043 scopus 로고
    • Construction and stability analysis of transition layer solutions in reaction-diffusion systems
    • Sakamoto K. Construction and stability analysis of transition layer solutions in reaction-diffusion systems. Tohoko Maht. J. 42:1990;17-44.
    • (1990) Tohoko Maht. J. , vol.42 , pp. 17-44
    • Sakamoto, K.1
  • 34
    • 0028743559 scopus 로고
    • Invariant manifolds and singularly perturbed boundary value problems
    • Tin S. K., Kopell N., Jones C. K. R. T. Invariant manifolds and singularly perturbed boundary value problems. SIAM J. Numer. Anal. 31:1994;1558-1576.
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 1558-1576
    • Tin, S.K.1    Kopell, N.2    Jones, C.K.R.T.3
  • 35
    • 0002011401 scopus 로고
    • The chemical basis of morphogenesis
    • Turing A. M. The chemical basis of morphogenesis. Phil. Trans. Roy. Soc. B. 237:1952;37-72.
    • (1952) Phil. Trans. Roy. Soc. B , vol.237 , pp. 37-72
    • Turing, A.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.