RT Journal Article
T1 On the growth of filamentary structures in planar media
A1 Andreucci, D.
A1 Herrero, Miguel A.
A1 Velázquez, J.J. L.
AB 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.
PB John Wiley and Sons
SN 0170-4214
YR 2004
FD 2004-11-10
LK https://hdl.handle.net/20.500.14352/50220
UL https://hdl.handle.net/20.500.14352/50220
LA eng
DS Docta Complutense
RD 13 jul 2025