ODE- and PDE-based modeling of biological transportation networks
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Applied Mathematics and Computational Science Program
Preprint Posting Date2018-05-22
Permanent link to this recordhttp://hdl.handle.net/10754/632527
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AbstractWe study the global existence of solutions of a discrete (ODE-based) model on a graph describing the formation of biological transportation networks, introduced by Hu and Cai. We propose an adaptation of this model so that a macroscopic (PDE-based) system can be obtained as its formal continuum limit. We prove the global existence of weak solutions of the macroscopic PDE model. Finally, we present results of numerical simulations of the discrete model, illustrating the convergence to steady states, their non-uniqueness as well as their dependence on initial data and model parameters.
CitationHaskovec, J., Kreusser, L. M., & Markowich, P. (2019). ODE- and PDE-based modeling of biological transportation networks. Communications in Mathematical Sciences, 17(5), 1235–1256. doi:10.4310/cms.2019.v17.n5.a4
SponsorsLMK was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) grant EP/L016516/1 and the German National Academic Foundation (Studienstiftung des Deutschen Volkes).
PublisherInternational Press of Boston