2024-04-24T12:22:58Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/502202023-08-11T02:14:23Zcom_20.500.14352_14col_20.500.14352_15
On the growth of filamentary structures in planar media
Andreucci, D.
Herrero, Miguel A.
Velázquez, J.J. L.
We analyse a mathematical model for the growth of thin filaments into a two dimensional medium. More exactly, we focus on a certain reaction/diffusion system, describing the interaction between three chemicals (an activator, an inhibitor and a growth factor), and including a fourth cell variable characterising irreversible incorporation to a filament. Such a model has been shown numerically to generate structures shaped like nets. We perform an asymptotical analysis of the behaviour of solutions, in the case when the system has parameters very large and very small, thereby allowing the onset of different time and space scales. In particular, we describe the motion of the tip of a filament, and the changes in the relevant chemical species nearby.
2023-06-20T09:42:26Z
2023-06-20T09:42:26Z
2004-11-10
journal article
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0170-4214
10.1002/mma.537
https://hdl.handle.net/20.500.14352/50220
http://onlinelibrary.wiley.com/doi/10.1002/mma.537/abstract
http://onlinelibrary.wiley.com
eng
restricted access
John Wiley and Sons