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Oberwolfach Reports

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Volume 15, Issue 3, 2018, pp. 2651–2701
DOI: 10.4171/OWR/2018/43

Published online: 2019-08-26

Differential Equations arising from Organising Principles in Biology

José A. Carrillo[1], Alexander Lorz[2], Anna Marciniak-Czochra[3] and Benoît Perthame[4]

(1) Imperial College London, UK
(2) King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia
(3) Mathematikon, Heidelberg, Germany
(4) Université Pierre et Marie Curie, Paris, France

This workshop brought together experts in modeling and analysis of organising principles of multiscale biological systems such as cell assemblies, tissues and populations. We focused on questions arising in systems biology and medicine which are related to emergence, function and control of spatial and inter-individual heterogeneity in population dynamics. There were three main areas represented of differential equation models in mathematical biology. The first area involved the mathematical description of structured populations. The second area concerned invasion, pattern formation and collective dynamics. The third area treated the evolution and adaptation of populations, following the Darwinian paradigm. These problems led to differential equations, which frequently are non-trivial extensions of classical problems. The examples included but were not limited to transport-type equations with nonlocal boundary conditions, mixed ODE-reaction-diffusion models, nonlocal diffusion and cross-diffusion problems or kinetic equations.

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Carrillo José, Lorz Alexander, Marciniak-Czochra Anna, Perthame Benoît: Differential Equations arising from Organising Principles in Biology. Oberwolfach Rep. 15 (2018), 2651-2701. doi: 10.4171/OWR/2018/43