| Abstract: |
| We are concerned with a shadow system of the Gierer-Meinhardt model in a finite interval. A stationary problem is studied and we consider the diffusion coefficient as a bifurcation parameter. A complete bifurcation diagram of the stationary solutions is obtained, and a stability of every stationary solution is determined. In particular, we show that all 1-mode solutions are stable for a small time constant and that other nontrivial solutions are unstable. The system is known for having stationary spiky patterns with large amplitude. Then, asymptotic expansions of maximum and minimum values of a stationary solution are also obtained. |
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