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# Peter Markowich : A PDE System Modeling Biological Network Formation

Transportation networks are ubiquitous as they are possibly the most important building blocks of nature. They cover microscopic and macroscopic length scales and evolve on fast to slow times scales. Examples are networks of blood vessels in mammals, genetic regulatory networks and signaling pathways in biological cells, neural networks in mammalian brains, venation networks in plant leafs and fracture networks in rocks. We present and analyze a PDE (Continuum) framework to model transportation networks in nature, consisting of a reaction-diffusion gradient-flow system for the network conductivity constrained by an elliptic equation for the transported commodity (fluid).

**Category**: Applied Math and Analysis**Duration**: 01:14:45**Date**: April 12, 2017 at 11:55 AM**Views**: 101-
**Tags:**seminar, Applied Math And Analysis Seminar

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