2020-03-29T06:06:50Z
http://oa.upm.es/cgi/oai2
oai:oa.upm.es:44788
2019-06-10T14:07:13Z
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Asymptotic stability of a two species chemotaxis system with non-diffusive chemoattractant
Tello del Castillo, José Ignacio
Negreanu Pruna, Mihaela
Biology
Mathematics
We study the behavior of two biological populations “u” and “v” attracted by the same chemical substance whose behavior is described in terms of second order parabolic equations. The model considers a logistic growth of the species and the interactions between them are relegated to the chemoattractant production. The system is completed with a third equation modeling the evolution of chemical. We assume that the chemical “w” is a non-diffusive substance and satisfies an ODE, more precisely,
{ut=Δu−∇⋅(uχ1(w)∇w)+μ1u(1−u),x∈Ω,t>0,vt=Δv−∇⋅(vχ2(w)∇w)+μ2v(1−v),x∈Ω,t>0,wt=h(u,v,w),x∈Ω,t>0,
under appropriate boundary and initial conditions in an n-dimensional open and bounded domain Ω. We consider the cases of positive chemo-sensitivities, not necessarily constant elements. The chemical production function h increases as the concentration of the species “u” and “v” increases. We first study the global existence and uniform boundedness of the solutions by using an iterative approach. The asymptotic stability of the homogeneous steady state is a consequence of the growth of h, χi and the size of μi. Finally, some examples of the theoretical results are presented for particular functions h and χi.
E.T.S.I de Sistemas Informáticos (UPM)
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
2015-03-05
info:eu-repo/semantics/article
Article
Journal of Differential Equations, ISSN 0022-0396, 2015-03-05, Vol. 258, No. 5
PeerReviewed
application/pdf
eng
http://www.sciencedirect.com/science/article/pii/S0022039614004458
MTM2013-42907
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jde.2014.11.009
http://oa.upm.es/44788/