WIAS Preprint No. 746, (2002)

Describing a class of global attractors via symbol sequences


  • Härterich, Jörg
  • Wolfrum, Matthias

2010 Mathematics Subject Classification

  • 35B40 34E15 37C29


  • singular perturbation, global attractor, transition layer, heteroclinic orbit


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 𝑘 subintervals, it is possible to characterize all stationary solutions for small ε by means of sequences of 𝑘 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 𝑘.

Appeared in

  • Discrete Contin. Dyn. Syst., 12, (2005) pp. 531-554

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