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dc.contributor.authorAlbi, Giacomo
dc.contributor.authorBurger, Martin
dc.contributor.authorHaskovec, Jan
dc.contributor.authorMarkowich, Peter A.
dc.contributor.authorSchlottbom, Matthias
dc.date.accessioned2017-05-31T11:23:07Z
dc.date.available2017-05-31T11:23:07Z
dc.date.issued2017-04-11
dc.identifier.citationAlbi G, Burger M, Haskovec J, Markowich P, Schlottbom M (2017) Continuum Modeling of Biological Network Formation. Modeling and Simulation in Science, Engineering and Technology: 1–48. Available: http://dx.doi.org/10.1007/978-3-319-49996-3_1.
dc.identifier.issn2164-3679
dc.identifier.issn2164-3725
dc.identifier.doi10.1007/978-3-319-49996-3_1
dc.identifier.urihttp://hdl.handle.net/10754/623812
dc.description.abstractWe present an overview of recent analytical and numerical results for the elliptic–parabolic system of partial differential equations proposed by Hu and Cai, which models the formation of biological transportation networks. The model describes the pressure field using a Darcy type equation and the dynamics of the conductance network under pressure force effects. Randomness in the material structure is represented by a linear diffusion term and conductance relaxation by an algebraic decay term. We first introduce micro- and mesoscopic models and show how they are connected to the macroscopic PDE system. Then, we provide an overview of analytical results for the PDE model, focusing mainly on the existence of weak and mild solutions and analysis of the steady states. The analytical part is complemented by extensive numerical simulations. We propose a discretization based on finite elements and study the qualitative properties of network structures for various parameter values.
dc.description.sponsorshipMB and MS acknowledge support by ERC via Grant EU FP 7 - ERC Con- solidator Grant 615216 LifeInverse. MB acknowledges support by the German Science Foundation DFG via EXC 1003 Cells in Motion Cluster of Excellence, Münster, Germany. GA acknowledges the ERC-Starting Grant project High-Dimensional Sparse Optimal Control (HDSPCONTR).
dc.publisherSpringer Nature
dc.relation.urlhttp://link.springer.com/chapter/10.1007/978-3-319-49996-3_1
dc.titleContinuum Modeling of Biological Network Formation
dc.typeBook Chapter
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalModeling and Simulation in Science, Engineering and Technology
dc.contributor.institutionApplied Numerical Analysis, Technical University of Munich, Boltzmannstr. 3, 85478, Garching bei München, Germany
dc.contributor.institutionInstitute for Computational and Applied Mathematics, University of Münster, Einsteinstr. 62, 48149, Münster, Germany
dc.contributor.institutionMultiscale Modeling and Simulation, University of Twente, P.O. Box 217, NL-7500, AE Enschede, The Netherlands
kaust.personHaskovec, Jan
kaust.personMarkowich, Peter A.
dc.date.published-online2017-04-11
dc.date.published-print2017


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