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Differential equations arising from organising principles in biology. Abstracts from the workshop held September 23–29, 2018. (English) Zbl 1425.00095

Summary: 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.

MSC:

00B05 Collections of abstracts of lectures
00B25 Proceedings of conferences of miscellaneous specific interest
35-06 Proceedings, conferences, collections, etc. pertaining to partial differential equations
92-06 Proceedings, conferences, collections, etc. pertaining to biology
35Q92 PDEs in connection with biology, chemistry and other natural sciences
37N25 Dynamical systems in biology
Full Text: DOI

References:

[1] M. Breden, R. Castelli; Existence and instability of steady states for a triangular crossdiffusion system : a computer-assisted proof, Journal of Differential Equations 264(10): 6418-6458, 2018. · Zbl 1458.35220
[2] M. Breden, J.-P. Lessard and M. Vanicat, Global bifurcation diagrams of steady states of systems of PDEs via rigorous numerics: a 3-component reaction-diffusion system, Acta Applicandae Mathematicae 128(1): 113-152, 2013. · Zbl 1277.65088
[3] X. Chen, E. S. Daus, A. J¨ungel, Global existence analysis of cross-diffusion population systems for multiple species, Arch. Ration. Mech. Anal. 227 (2) (2018) 715-747. · Zbl 1384.35135
[4] Esther Daus, Laurent Desvillettes and Helge Dietert, About the entropic structure of detailed balanced multi-species cross-diffusion equations, to appear in J. Diff. Eq. · Zbl 1405.35082
[5] Laurent Desvillettes, Ariane Trescases, New results for triangular reaction cross diffusion systems, Journal of Mathematical Analysis and Applications, 430, n.1, (2015), 32-59. · Zbl 1319.35077
[6] Iida, Masato; Mimura, Masayasu; Ninomiya, Hirokazu, Diffusion, cross-diffusion and competitive interaction, J. Math. Biol. 53 (2006), no. 4, 617-641. · Zbl 1113.92064
[7] Shigesada, Nanako; Kawasaki, Kohkichi; Teramoto, Ei, Spatial segregation of interacting species, J. Theoret. Biol. 79 (1979), no. 1, 83-99. · Zbl 0688.92016
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