| Abstract: |
| The collective motion of camphor boats in the water channel exhibits both a homogeneous and an inhomogeneous state, depending on the number of boats. The motion of each boat is described by a traveling pulse in a reaction-diffusion model proposed in Nagayama et al. (2004), in which boats are assumed to interact each other by the change of surface tension by diffusive molecules on the water surface. In order to study the inhomogeneous motion of camphor boats, we have to treat the linearized eigenvalue problem. However, the eigenvalue problem is too difficult to analyze. Then we would like to derive a reduced system from the original model and analyze it by applying the center manifold theorem.
Several reaction-diffusion systems can generate a solution with a pulse shape. Pulse-pulse interaction is treated mathematically in Ei et al. (2002), in which a reduced system is derived from a reaction-diffusion model by applying a center manifold theorem. Since the delta functions naturally arise in our model, the theory established in L2-framework cannot be applied directly. In this talk, we modify the previous results in Ei et al. (2002) and propose a new approach of reduction to systems with the delta function. |
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