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Stability analysis of reaction-diffusion models on evolving domains: the effects of cross-diffusion

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dc.contributor.authorMadzvamuse, Anotida
dc.contributor.authorNdakwo, Hussaini
dc.contributor.authorBarreira, Raquel
dc.date.accessioned2018-04-09T13:13:41Z
dc.date.available2018-04-09T13:13:41Z
dc.date.issued2016
dc.description.abstractThis article presents stability analytical results of a two compo-nent reaction-diffusion system with linear cross-diffusion posed on continuouslyevolving domains. First the model system is mapped from a continuously evolv-ing domain to a reference stationary frame resulting in a system of partialdifferential equations with time-dependent coefficients. Second, by employingappropriately asymptotic theory, we derive and prove cross-diffusion-driven in-stability conditions for the model system for the case of slow, isotropic domaingrowth. Our analytical results reveal that unlike the restrictive diffusion-driveninstability conditions on stationary domains, in the presence of cross-diffusioncoupled with domain evolution, it is no longer necessary to enforce cross norpure kinetic conditions. The restriction toactivator-inhibitorkinetics to inducepattern formation on a growing biological system is no longer a requirement.Reaction-cross-diffusion models with equal diffusion coefficients in the principalcomponents as well as those of theshort-range inhibition, long-range activa-tionandactivator-activatorform can generate patterns only in the presence ofcross-diffusion coupled with domain evolution. To confirm our theoretical find-ings, detailed parameter spaces are exhibited for the special cases of isotropicexponential, linear and logistic growth profiles. In support of our theoreticalpredictions, we present evolving or moving finite element solutions exhibitingpatterns generated by ashort-range inhibition, long-range activationreaction-diffusion model with linear cross-diffusion in the presence of domain evolution.pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.citationMadzvamuse, A., Ndakwo, H.S., Barreira, R. (2016). Stability analysis of reaction-diffusion models on evolving domains: The effects of cross-diffusion. Discrete and Continuous Dynamical Systems - A, 36 (4), pp. 2133–2170. doi: 10.3934/dcds.2016.36.2133pt_PT
dc.identifier.doi10.3934/dcds.2016.36.2133pt_PT
dc.identifier.urihttp://hdl.handle.net/10400.26/22216
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.relationResearch Training Network on Integrated Component Cycling in Epithelial Cell Motility
dc.titleStability analysis of reaction-diffusion models on evolving domains: the effects of cross-diffusionpt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.awardTitleResearch Training Network on Integrated Component Cycling in Epithelial Cell Motility
oaire.awardURIinfo:eu-repo/grantAgreement/EC/H2020/642866/EU
oaire.citation.titleDiscrete and Continuous Dynamical Systems - Series Apt_PT
oaire.fundingStreamH2020
person.familyNameBarreira
person.givenNameRaquel
person.identifier.ciencia-id011B-AC27-378A
person.identifier.orcid0000-0002-8326-1593
project.funder.identifierhttp://doi.org/10.13039/501100008530
project.funder.nameEuropean Commission
rcaap.rightsclosedAccesspt_PT
rcaap.typearticlept_PT
relation.isAuthorOfPublication11adc260-5103-4d3a-887f-6ae77108f173
relation.isAuthorOfPublication.latestForDiscovery11adc260-5103-4d3a-887f-6ae77108f173
relation.isProjectOfPublication1425233e-9504-4955-9eff-1c9db04d757d
relation.isProjectOfPublication.latestForDiscovery1425233e-9504-4955-9eff-1c9db04d757d

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