| Contents |
| We study various temporal and spatial discretization
methods for bistable reaction-diffusion problems. The main focus
is on the functional differential operators that arise after linearizing
around travelling waves in the spatially discrete problem
and studying how the subsequent discretization of time affects
the spectral properties of these operators.
This represents a highly singular perturbation that we attempt
to understand via a weak-limit method based on the pioneering
work of Bates, Chen and Chmaj (2003). Once this perturbation is
understood, one can study the existence and (non)-uniqueness
of waves in the fully discretized reaction-diffusion system. |
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