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Description:
We study a singularly perturbed scalar reaction-diffusion equation on a bounded interval with a spatially inhomogeneous bistable nonlinearity. For certain nonlinearities, which are piecewise constant in space on 푘 subintervals, it is possible to characterize all stationary solutions for small ε by means of sequences of 푘 symbols, indicating the behavior of the solution in each subinterval. Determining also Morse-indices and zero numbers of the equilibria in terms of the symbol sequences, we are able to give a criterion for heteroclinic connections and a description of the associated global attractor for all 푘.