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- W3134848692 abstract "Abstract In this paper we consider an adaptive spatial discretization scheme for the Nagumo PDE. The scheme is a commonly used spatial mesh adaptation method based on equidistributing the arclength of the solution under consideration. We assume that this equidistribution is strictly enforced, which leads to the non-local problem with infinite range interactions that we derived in Hupkes and Van Vleck (J Dyn Differ Equ 28:955, 2016). For small spatial grid-sizes, we establish some useful Fredholm properties for the operator that arises after linearizing our system around the travelling wave solutions to the original Nagumo PDE. In particular, we perform a singular perturbation argument to lift these properties from the natural limiting operator. This limiting operator is a spatially stretched and twisted version of the standard second order differential operator that is associated to the PDE waves." @default.
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- W3134848692 date "2021-03-06" @default.
- W3134848692 modified "2023-09-27" @default.
- W3134848692 title "Travelling Waves for Adaptive Grid Discretizations of Reaction Diffusion Systems II: Linear Theory" @default.
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- W3134848692 doi "https://doi.org/10.1007/s10884-021-09942-y" @default.
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