Abstract
AbstractIn this paper we consider a spatial discretization scheme with an adaptive grid for the Nagumo PDE and establish the existence of travelling waves. In particular, we consider the time dependent spatial mesh adaptation method that aims to equidistribute 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 Eqn, 2021). Using the Fredholm theory developed in Hupkes and Van Vleck (J Dyn Differ Eqn, 2021) we setup a fixed point procedure that enables the travelling PDE waves to be lifted to our spatially discrete setting.
Funder
National Science Foundation
Nederlandse Organisatie voor Wetenschappelijk Onderzoek
Publisher
Springer Science and Business Media LLC
Cited by
1 articles.
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1. Learning of discrete models of variational PDEs from data;Chaos: An Interdisciplinary Journal of Nonlinear Science;2024-01-01