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On the growth of filamentary structures in planar media

Andreucci, D. and Herrero, Miguel A. and Velázquez, J.J. L. (2004) On the growth of filamentary structures in planar media. Mathematical Methods in the Applied Sciences, 27 (16). pp. 1935-1968. ISSN 0170-4214

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Abstract

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.


Item Type:Article
Uncontrolled Keywords:Biological pattern-formation; Gierer-Meinhardt system; positive solutions; capillary formation; spike; angiogenesis; uniqueness; equations; dynamics; model; reaction-diffusion systems; asymptotic behaviour of solutions; singular perturbation techniques; mathematical biology
Subjects:Medical sciences > Biology > Biomathematics
Sciences > Mathematics > Differential equations
ID Code:17331
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