Tohoku Mathematical Journal

Construction and stability analysis of transition layer solutions in reaction-diffusion systems

Kunimochi Sakamoto

Full-text: Open access

Article information

Tohoku Math. J. (2) Volume 42, Number 1 (1990), 17-44.

First available in Project Euclid: 3 May 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K57: Reaction-diffusion equations


Sakamoto, Kunimochi. Construction and stability analysis of transition layer solutions in reaction-diffusion systems. Tohoku Math. J. (2) 42 (1990), no. 1, 17--44. doi:10.2748/tmj/1178227692.

Export citation


  • [1] S. ANGENENT, J. MALLET-PARET AND L. PELETIER, Stable transition layers in a semilinear boundary value problems, J. Differential Equations 67 (1987), 212-242.
  • [2] S. N. CHOW AND J. K. HALE, "Methods of Bifurcation Theory" Springer-Verlag, 1983
  • [3] E. CONWAY, D. HOFF AND J. SMOLLER, Large time behavior of solutions of systems of reaction diffusio equations, SIAMJ. Appl. Math. 35 (1978), 1-16.
  • [4] P. C. FIFE, Transition layers in singular perturbation problems, J. Differential Equations 15 (1974), 77-105.
  • [5] P. C. FIFE, Boundary and interior transition layer phenomena for pairs of second-order differentia equations, J. Math. Anal. App. 54 (1976), 497-521.
  • [6] H. FUJII AND Y. HOSONO, Neumann layer phenomena in nonlinear diffusion systems, Lecture Notes i Num.Anal. 6 (1983), 21-38.
  • [7] H. FUJII, M. MIMURA AND Y. NISHIURA, A picture of the global bifurcation diagram in ecologica interacting and diffusing systems, Physica 5D (1982), 1-42.
  • [8] H. FUJ AND Y. NISHIURA, Stability of singularly perturbed solutions to systems of reaction-diffusio equations, SIAM J. of Math. Anal. 18 (1987), 1726-1770.
  • [9] J. K. HALE, Large diffusivity and asymptotic behavior in parabolic systems, J. Math. Anal. App. 11 (1986), 455-466.
  • [10] J. K. HALE AND C. ROCHA, Varying boundary conditions with large diffusivity, J. Math. Pures et Appl 66 (1987), 139-158.
  • [11] J. K. HALE AND K. SAKAMOTO, Existence and stability of transition layers, Japan Journal of App. Math 5 (1988), 367-405.
  • [12] M. Io, A remark on singular perturbation, Hiroshima Math. Journal 14 (1984), 619-629
  • [13] M. MIMURA, M. TABATA AND Y. HOSONO, Multiple solutions of two-point boundary value problems o Neumann type with a small parameter, SIAM J. Math. Anal. 11 (1980), 613-631.
  • [14] Y. NISHIURA, H. FUJ AND Y. HOSONO, On the structure of multiple existence of stable stationar solutions in systems of reaction-diffusion equations – a survey, in "Patterns and Waves, " Eds. Nishida, Mimura and Fuj, North-Holland, (1987), 157-220.
  • [15] Y. NISHIURA, Globalstructureof bifurcating solutions of some reaction-diffusion systems, SIAM J. Math Anal. 13 (1982), 555-593.
  • [16] Y. NISHIURA, H. FUJII, SLEP method to the stability of singularly perturbed solutions with multipl transition layers in reaction-diffusion systems, in "Dynamics of Infinite Dimensional Systems, " Eds. J. K. Hale and S. N. Chow, Springer-Verlag, 1987.
  • [17] K. SAKAMOTO, The existence and the stability properties of transition layer solutions in singularl perturbed ordinary differential equations, Ph.D dissertation, Brown University, 1988.