Abstract
A general class of reaction-diffusion systems is considered; this includes a large family of models for chemical activity on isothermal catalyst surfaces. Necessary and sufficient conditions are given for when a stable, spatially nonuniform solution can bifurcate from a steady uniform solution as parameters in the equations are varied. In particular, such a bifurcation occurs for the Dirichlet problem but not for the Neumann problem. A rather complete description is given concerning the stability properties, direction of bifurcation, and global continuation of the branch of bifurcating solutions.
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