Publication:
On the growth of filamentary structures in planar media

dc.contributor.authorAndreucci, D.
dc.contributor.authorHerrero, Miguel A.
dc.contributor.authorVelázquez, J.J. L.
dc.date.accessioned2023-06-20T09:42:26Z
dc.date.available2023-06-20T09:42:26Z
dc.date.issued2004-11-10
dc.description.abstractWe 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.
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/17331
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dc.identifier.doi10.1002/mma.537
dc.identifier.issn0170-4214
dc.identifier.officialurlhttp://onlinelibrary.wiley.com/doi/10.1002/mma.537/abstract
dc.identifier.relatedurlhttp://onlinelibrary.wiley.com
dc.identifier.urihttps://hdl.handle.net/20.500.14352/50220
dc.issue.number16
dc.journal.titleMathematical Methods in the Applied Sciences
dc.language.isoeng
dc.page.final1968
dc.page.initial1935
dc.publisherJohn Wiley and Sons
dc.rights.accessRightsrestricted access
dc.subject.cdu517.956.4
dc.subject.cdu539.2
dc.subject.cdu51-76
dc.subject.keywordBiological pattern-formation
dc.subject.keywordGierer-Meinhardt system
dc.subject.keywordpositive solutions
dc.subject.keywordcapillary formation
dc.subject.keywordspike
dc.subject.keywordangiogenesis
dc.subject.keyworduniqueness
dc.subject.keywordequations
dc.subject.keyworddynamics
dc.subject.keywordmodel
dc.subject.keywordreaction-diffusion systems
dc.subject.keywordasymptotic behaviour of solutions
dc.subject.keywordsingular perturbation techniques
dc.subject.keywordmathematical biology
dc.subject.ucmBiomatemáticas
dc.subject.ucmEcuaciones diferenciales
dc.subject.unesco2404 Biomatemáticas
dc.subject.unesco1202.07 Ecuaciones en Diferencias
dc.titleOn the growth of filamentary structures in planar media
dc.typejournal article
dc.volume.number27
dspace.entity.typePublication
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