• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.371-387
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• 1995

Let X be a compact polyhedron, H a normal subgroup of the fundamental group $\pi_1(X)$ of X and $f : X \longrightarrow X$ a selfmap such that $f_piH \subset H$, where f_\pi : \pi_1(X) \longrightarrow \pi_1(X)$ is the induced homomorphism by f.

• Journal of the Korean Mathematical Society
• /
• v.32 no.3
• /
• pp.389-399
• /
• 1995

We consider the reaction-diffusion system of two-component model in one-dimensional space described by $$ (1) u_s = d_1 u_{xx} + f(u, \upsilon) \upsilon_t = d_2\upsilon_{xx} + \gammag(u, \upsilon) $$ where $d_1$ and $d_2$ are the diffusion rates of u and $\upsilon$, and $\gamma$ is the ration of reaction rates. It is interesting the case of that there are differences in the diffusion and reaction rates of u and $\upsilon$.