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