ODE-and PDE-based modeling of biological transportation networks
Accepted version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Haskovec, J
Kreusser, LM
Markowich, P
Abstract
We 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.
Description
Keywords
Weak solutions, energy dissipation, continuum limit, pattern formation, numerical modeling
Journal Title
Communications in Mathematical Sciences
Conference Name
Journal ISSN
1539-6746
1945-0796
1945-0796
Volume Title
17
Publisher
International Press of Boston
Publisher DOI
Rights
All rights reserved