Multi-dimensional transition layers for an exothermic reaction-diffusion system in long cylindrical domains

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概要

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• 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.

• 東京大学の論文

著者

• Mimura Masanao

  Department Of Physics Faculty Of Science Okayama University:central Research Laboratory The Furukawa

• Mimura M

  Department Of Mathematics Faculty Of Science Hiroshima University

• Mimura Masayasu

  Graduate School of Mathematical Sciences, The University of Tokyo

• Sakamoto Kunimochi

  Department of Mathematics, Faculty of Science, Hiroshima University

• Mimura Masayasu

  Graduate School Of Mathematical Sciences The University Of Tokyo

• Sakamoto Kunimochi

  Department Of Mathematical And Life Sciences Graduate School Of Science Hiroshima University

• Sakamoto Kunimochi

  Department Of Mathematics Faculty Of Science Hiroshima University

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