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Volumn 200, Issue 3-4, 2005, Pages 325-358

The existence and stability of travelling waves with transition layers for some singular cross-diffusion systems

Author keywords

Cross diffusion system; Existence; Spectral; Stability; Travelling; Unstable bundle

Indexed keywords

ASYMPTOTIC STABILITY; EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL MODELS; PERTURBATION TECHNIQUES; PROBLEM SOLVING; SPECTRUM ANALYSIS; SYSTEM STABILITY; THEOREM PROVING; TOPOLOGY;

EID: 12244304894     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2004.11.010     Document Type: Article
Times cited : (23)

References (28)
  • 1
    • 0005235678 scopus 로고
    • A topological invariant arising in the stability analysis of travelling waves
    • J. Alexsander, R.A. Gardner, C.K.R.T. Jones, A topological invariant arising in the stability analysis of travelling waves, J. Die Reine Angewandte Math. 410 (1990) 167-212.
    • (1990) J. Die Reine Angewandte Math. , vol.410 , pp. 167-212
    • Alexsander, J.1    Gardner, R.A.2    Jones, C.K.R.T.3
  • 2
    • 84972541997 scopus 로고
    • Dynamic theory of quasilinear parabolic equations. II. Reaction-diffusion systems
    • H. Amann, Dynamic theory of quasilinear parabolic equations. II. Reaction-diffusion systems, Differential Integral Eqs. 3 (1990) 13-75.
    • (1990) Differential Integral Eqs. , vol.3 , pp. 13-75
    • Amann, H.1
  • 3
    • 85087535076 scopus 로고    scopus 로고
    • A stability index analysis of 1D patterns of the Gray-Scott model
    • A. Doleman, R.A. Gardner, T.J. Kaper, A stability index analysis of 1D patterns of the Gray-Scott model, Memoirs AMS 155 (737) (2002) 1-64.
    • (2002) Memoirs AMS , vol.155 , Issue.737 , pp. 1-64
    • Doleman, A.1    Gardner, R.A.2    Kaper, T.J.3
  • 4
    • 38249005979 scopus 로고
    • The principle of linearized stability for quasilinear parabolic evolution equations
    • A.K. Drangeid, The principle of linearized stability for quasilinear parabolic evolution equations, Nonl. Anal. TMA 13 (1989) 1091-1113.
    • (1989) Nonl. Anal. TMA , vol.13 , pp. 1091-1113
    • Drangeid, A.K.1
  • 5
    • 34250627892 scopus 로고
    • Geometric singular perturbation theory
    • N. Fenichel, Geometric singular perturbation theory, J. Differential Eqs. 31 (1979) 53-98.
    • (1979) J. Differential Eqs. , vol.31 , pp. 53-98
    • Fenichel, N.1
  • 6
    • 12244281026 scopus 로고
    • Topological methods arising in the study of travelling waves
    • Clarendon Press, Oxford
    • R.A. Gardner, Topological methods arising in the study of travelling waves, in: Reaction-Diffusion Equations, Clarendon Press, Oxford, 1990, pp. 173-198.
    • (1990) Reaction-Diffusion Equations , pp. 173-198
    • Gardner, R.A.1
  • 7
    • 0010760437 scopus 로고    scopus 로고
    • Instability of oscillatory shock profile solutions of the generalized Burgers-Kdv equations
    • R.A. Gardner, Instability of oscillatory shock profile solutions of the generalized Burgers-Kdv equations, Physica D 90 (1996) 366-386.
    • (1996) Physica D , vol.90 , pp. 366-386
    • Gardner, R.A.1
  • 8
    • 84966244631 scopus 로고
    • Stability of travelling wave solutions of diffusive predator-prey systems
    • R.A. Gardner, C.R.K.T. Jones, Stability of travelling wave solutions of diffusive predator-prey systems, Trans. Am. Soc. 327 (1991) 465-524.
    • (1991) Trans. Am. Soc. , vol.327 , pp. 465-524
    • Gardner, R.A.1    Jones, C.R.K.T.2
  • 9
    • 0004188206 scopus 로고
    • Springer-Verlag, New York, Heidelberg, Berlin
    • M. Hirsch, Differential Topology, Springer-Verlag, New York, Heidelberg, Berlin, 1976.
    • (1976) Differential Topology
    • Hirsch, M.1
  • 10
    • 0000167408 scopus 로고
    • Singular perturbation approach to travelling waves in competing and diffusion species models
    • Y. Hosono, M. Mimura, Singular perturbation approach to travelling waves in competing and diffusion species models, J. Math. Kyoto Univ. 22 (1982) 435-461.
    • (1982) J. Math. Kyoto Univ. , vol.22 , pp. 435-461
    • Hosono, Y.1    Mimura, M.2
  • 11
    • 0012988399 scopus 로고
    • Travelling waves for some biological systems with density dependent diffusion
    • Y. Hosono, Travelling waves for some biological systems with density dependent diffusion, Jpn. J. Appl. Math. 4 (1987) 297-359.
    • (1987) Jpn. J. Appl. Math. , vol.4 , pp. 297-359
    • Hosono, Y.1
  • 13
    • 0000653552 scopus 로고
    • Global bifurcation phenomena of travelling wave solutions for some bistable reaction-diffusion systems
    • H. Ikeda, M. Mimura, Y. Nishiura, Global bifurcation phenomena of travelling wave solutions for some bistable reaction-diffusion systems, Nonl. Anal. TMA 13 (1989) 507-526.
    • (1989) Nonl. Anal. TMA , vol.13 , pp. 507-526
    • Ikeda, H.1    Mimura, M.2    Nishiura, Y.3
  • 14
    • 0002316532 scopus 로고
    • Geometric singular perturbation theory
    • Springer-Verlag, Berlin
    • C.K.R.T. Jones, Geometric Singular Perturbation Theory. Lecture Notes in Mathematics, vol. 1609, Springer-Verlag, Berlin, 1995, pp. 44-118.
    • (1995) Lecture Notes in Mathematics , vol.1609 , pp. 44-118
    • Jones, C.K.R.T.1
  • 15
    • 84967743294 scopus 로고
    • Stability of the travelling wave solution of the Fitzhugh-Nagumo system
    • C.K.R.T. Jones, Stability of the travelling wave solution of the Fitzhugh-Nagumo system, Trans. Am. Math. Soc. 286 (1984) 431-469.
    • (1984) Trans. Am. Math. Soc. , vol.286 , pp. 431-469
    • Jones, C.K.R.T.1
  • 16
    • 54649084116 scopus 로고    scopus 로고
    • Existence of standing pulse solutions to an inhomogeneous reaction-diffusion system
    • C.K.R.T. Jones, J.E. Rubin, Existence of standing pulse solutions to an inhomogeneous reaction-diffusion system, J. Dyn. Differential Eqs. 10 (1998) 1-35.
    • (1998) J. Dyn. Differential Eqs. , vol.10 , pp. 1-35
    • Jones, C.K.R.T.1    Rubin, J.E.2
  • 17
    • 84972514721 scopus 로고
    • Stability of singularly perturbed solutions to nonlinear diffusion systems arising in population dynamics
    • Y. Kan-on, Stability of singularly perturbed solutions to nonlinear diffusion systems arising in population dynamics, Hiroshima Math. J. 23 (1993) 509-536.
    • (1993) Hiroshima Math. J. , vol.23 , pp. 509-536
    • Kan-on, Y.1
  • 18
    • 0001969945 scopus 로고    scopus 로고
    • Existence and stability of singular heteroclinic orbits for the Ginzburg-Landau equation
    • T. Kapitula, Existence and stability of singular heteroclinic orbits for the Ginzburg-Landau equation, Nonlinearity 9 (1996) 669-685.
    • (1996) Nonlinearity , vol.9 , pp. 669-685
    • Kapitula, T.1
  • 19
    • 0033130048 scopus 로고    scopus 로고
    • Diffusion vs. cross-diffusion: An elliptic approach
    • Y. Lou, W.-M. Ni, Diffusion vs. cross-diffusion: an elliptic approach, J. Differential Eqs. 154 (1999) 157-190.
    • (1999) J. Differential Eqs. , vol.154 , pp. 157-190
    • Lou, Y.1    Ni, W.-M.2
  • 20
    • 22644451162 scopus 로고    scopus 로고
    • Stability of non-monotone waves in a three-species reaction-diffusion model
    • P.D. Miller, Stability of non-monotone waves in a three-species reaction-diffusion model, Proc. R Soc. Edinburgh, Sect. A 129 (1999) 125-152.
    • (1999) Proc. R Soc. Edinburgh, Sect. A , vol.129 , pp. 125-152
    • Miller, P.D.1
  • 21
    • 0013322639 scopus 로고
    • Singular limit analysis of stability of travelling wave solutions in bistable reaction-diffusion systems
    • Y. Nishiura, M. Mimura, H. Ikeda, H. Fuji, Singular limit analysis of stability of travelling wave solutions in bistable reaction-diffusion systems, SIAM J. Math Anal. 2 (1990) 85-122.
    • (1990) SIAM J. Math Anal. , vol.2 , pp. 85-122
    • Nishiura, Y.1    Mimura, M.2    Ikeda, H.3    Fuji, H.4
  • 23
    • 12244273201 scopus 로고    scopus 로고
    • Stability, bifurcation and edge oscillations in standing solutions to an inhomogeneous reaction-diffusion system
    • J.E. Rubin, Stability, bifurcation and edge oscillations in standing solutions to an inhomogeneous reaction-diffusion system, Proc. R. Soc. Edinburgh, Sect. A 129 (1999) 1033-1079.
    • (1999) Proc. R. Soc. Edinburgh, Sect. A , vol.129 , pp. 1033-1079
    • Rubin, J.E.1
  • 25
    • 44949272344 scopus 로고
    • Transversal heteroclinic and homoclinic orbits in singular perturbation problems
    • P. Szmolyan, Transversal heteroclinic and homoclinic orbits in singular perturbation problems, J. Differential Eqs. 92 (1991) 252-281.
    • (1991) J. Differential Eqs. , vol.92 , pp. 252-281
    • Szmolyan, P.1
  • 26
    • 0003102916 scopus 로고
    • Travelling waves for a class of cross-diffusion systems with small parameters
    • Y. Wu, Travelling waves for a class of cross-diffusion systems with small parameters, J. Differential Eqs. 123 (1995) 1-34.
    • (1995) J. Differential Eqs. , vol.123 , pp. 1-34
    • Wu, Y.1
  • 27
    • 12244293576 scopus 로고    scopus 로고
    • The existence of travelling waves for a cross-diffusion system with small parameter
    • Y. Wu, The existence of travelling waves for a cross-diffusion system with small parameter, Beijing Math. 3 (1997) 74-85.
    • (1997) Beijing Math. , vol.3 , pp. 74-85
    • Wu, Y.1
  • 28
    • 12244312962 scopus 로고    scopus 로고
    • The instability of spiky steady states for a competing species model with cross-diffusion
    • in press
    • Y. Wu, The instability of spiky steady states for a competing species model with cross-diffusion, J. Differential Eqs., in press.
    • J. Differential Eqs.
    • Wu, Y.1


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