Effect of boundary conditions on the dynamics of a pulse
solution for reaction-diffusion systems

Shin-Ichiro Ei; Toshio Ishimoto; Shin-Ichiro Ei; Toshio Ishimoto

doi:10.3934/nhm.2013.8.191

Networks and Heterogeneous Media

2013, Volume 8, Issue 1: 191-209. doi: 10.3934/nhm.2013.8.191

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Effect of boundary conditions on the dynamics of a pulse solution for reaction-diffusion systems

Shin-Ichiro Ei ^{1
,},
Toshio Ishimoto ^{2
,}

1.
Institute of Mathematics for Industry, Kyusyu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395
2.
Opinion Poll Research Center, The Asahi Shimbun Company, Tokyo 104-8011

Received: 01 February 2012 Revised: 01 January 2013
Primary: 35K57; Secondary: 35B25, 35K55.

We consider pulse-like localized solutions for reaction-diffusion systems on a half line and impose various boundary conditions at one end of it. It is shown that the movement of a pulse solution with the homogeneous Neumann boundary condition is completely opposite from that with the Dirichlet boundary condition. As general cases, Robin type boundary conditions are also considered. Introducing one parameter connecting the Neumann and the Dirichlet boundary conditions, we clarify the transition of motions of solutions with respect to boundary conditions.
- Reaction-diffusion systems,
- effect of boundary conditions,
- pulse solutions,
- front solutions
Citation: Shin-Ichiro Ei, Toshio Ishimoto. Effect of boundary conditions on the dynamics of a pulsesolution for reaction-diffusion systems[J]. Networks and Heterogeneous Media, 2013, 8(1): 191-209. doi: 10.3934/nhm.2013.8.191

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Abstract

We consider pulse-like localized solutions for reaction-diffusion systems on a half line and impose various boundary conditions at one end of it. It is shown that the movement of a pulse solution with the homogeneous Neumann boundary condition is completely opposite from that with the Dirichlet boundary condition. As general cases, Robin type boundary conditions are also considered. Introducing one parameter connecting the Neumann and the Dirichlet boundary conditions, we clarify the transition of motions of solutions with respect to boundary conditions.

References

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