| Abstract: |
| The linearized eigenvalue problems for stationary solutions of the 1-dimensional reaction-diffusion
systems are considered. In the single equation case with special nonlinearities and the homogeneous Neumann boundary condition, S. Yotsutani and the author has obtained all of eigenfunctions in terms of elliptic functions, and have classified them through the asymptotic properties on eigenpairs when the diffusion coefficient is sufficiently small.
In this talk we will consider the asymptotic propertieson eigenpairs associated with $n$-layers/spikes stationary
solutions for a wider class of reaction-diffusion system.Using a dynamical system approach by Ei (2002), we will derive
the asymptotic formulas for the critical $n$ eigenpairs, which characterize stability of each steady-state from dynamical point of view. |
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