The MathNet Korea
Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Journal of Mathematical Sciences. The University of Tokyo
( Vol. 3 NO.1 / (1996))
Multi-Dimensional Transition Layers for an Exothermic Reaction-Diffusion System in Long Cylindrical Domains
Masayasu Mimura, Kunimochi Sakamoto,
Pages. 109-179
Abstract By using singular perturbation techniques, it is shown that an
exothermal reaction-diffusion system with a small parameter in long cylindrical
domains admits a family of transition layer solutions. The solutions exhibit
spatial inhomogeneity in two directions, one in the axis of the cylinder and the
other in the cross-sectional direction is determined by a family of solutions of
a non-linear elliptic eigenvalue problem, called $the ; perturbed ; Gelfand
;problem$. On the other hand, the profile of the solutions in the axial
direction of the cylindrical domain has a sharp transition layer. The stability
analysis is also carried out for the equilibrium solutions, which reveals that a
Hopf-bifurcation occurs as some control parameters are varied, exhibiting
spatio-temporal oscillations.
Contents 1. Introduction
2. Approximation
2.1. Outer solutions
2.2. Inner solutions
3. Proof of theorem A
3.1. Spectral analysis
3.2. Existence of solutions
4. Proof of theorem B
5. Concluding remarks
6. Appendix
Key words
Mathmatical Subject Classification 35B25, 35B4, 35K57