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 タイトル: Multi-dimensional transition layers for an exothermic reaction-diffusion system in long cylindrical domains 著者: Mimura, MasayasuSakamoto, Kunimochi 発行日: 1996年 出版者: Graduate School of Mathematical Sciences, The University of Tokyo 掲載誌情報: Journal of Mathematical Sciences, The University of Tokyo. Vol. 3 (1996), No. 1, Page 109-179 抄録: 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-section of the cylindrical domain. The profile of the solutions in the cross-sectional direction is determined by a family of solutions of a non-linear elliptic eigenvalue problem, called {\it 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. URI: http://hdl.handle.net/2261/1543 ISSN: 13405705 出現カテゴリ: Journal of Mathematical Sciences, the University of TokyoJournal of Mathematical Sciences, the University of Tokyo

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