Target pattern solutions to reaction-diffusion equations in the presence of impurities

We consider reaction-diffusion equations of the special type

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having compact support in x. Assumptions about the relevant space scales and size of the catalytic effect exactly parallel those of Hagan (Advances in Appl. Math., 2 (1981), 400–416). The results are also parallel: For x of dimension one or two, if Ω(x) ≥ 0, Ω 0, then a unique target pattern solution which stays locally close to the homogeneous limit cycle solution. If x has dimension three, there is such a solution provided that Ω(x) is sufficiently large. Thus this paper shows that the phenomena uncovered formally by Hagan for a much larger class of kinetic equations can be rigorously substantiated for λ — ω systems.