Effect of boundary conditions on the dynamics of a pulse
solution for reaction-diffusion systems
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1.
Institute of Mathematics for Industry, Kyusyu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395
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2.
Opinion Poll Research Center, The Asahi Shimbun Company, Tokyo 104-8011
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Received:
01 February 2012
Revised:
01 January 2013
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Primary: 35K57; Secondary: 35B25, 35K55.
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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.
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.
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