On modelling biological network formation

11 Jul 2018, 11:00
New Law School/--100 (University of Sydney)

New Law School/--100

University of Sydney

Oral Presentation Minisymposium: Nonlinear PDE models in life and social sciences Nonlinear PDE models in life and social sciences


Helene Ranetbauer (University of Vienna)


In this talk we present a mesoscopic model for natural network formation processes, acting as a bridge between a discrete and continuous network approach proposed by Hu and Cai. All models describe the pressure field and the dynamics of the conductance network under pressure force effects.

We start by presenting the different approaches and analyze their corresponding properties. We will focus on special stationary solutions of the mesoscopic model including discrete network solutions.

This involves a proper reinterpretation of the system in terms of measure valued solutions. To overcome the arising difficulties, we will also introduce an alternative formulation replacing the nonlinear Poisson equation for the pressure field in the original approach by a linear side constraint.

Primary author

Helene Ranetbauer (University of Vienna)

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