Andreucci, D. y Herrero, Miguel A. y 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
![]() |
PDF
Restringido a Sólo personal autorizado del repositorio hasta 31 Diciembre 2020. 266kB |
URL Oficial: http://onlinelibrary.wiley.com/doi/10.1002/mma.537/abstract
URL | Tipo de URL |
---|---|
http://onlinelibrary.wiley.com | Editorial |
Resumen
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.
Tipo de documento: | Artículo |
---|---|
Palabras clave: | 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 |
Materias: | Ciencias Biomédicas > Biología > Biomatemáticas Ciencias > Matemáticas > Ecuaciones diferenciales |
Código ID: | 17331 |
Depositado: | 05 Dic 2012 09:21 |
Última Modificación: | 07 Feb 2014 09:45 |
Descargas en el último año
Sólo personal del repositorio: página de control del artículo