Analysis of a onedimensional foragerexploiter model
Abstract
\begin{abstract} \noindent % We consider the onedimensional parabolic system The system \bas \left\{ \begin{array}{l} u_t= u_{xx}  \chi_1 (uw_x)_x, \\[1mm] v_t = v_{xx}  \chi_2 (vu_x)_x, \\[1mm] w_t = dw_{xx}  \lambda (u+v)w  \mu w + r, \end{array} \right. \eas % that has been proposed as a model to describe social interactions within mixed foragerexploiter groups. is considered in a bounded real interval, with positive parameters $\chi_1,\chi_2,d,\lambda$ and $\mu$, and with $r \ge 0$. Proposed to describe social interactions within mixed foragerexploiter groups, this model extends classical onespecies chemotaxisconsumption systems by additionally accounting for a second axis mechanism coupled to the first in a consecutive manner. \abs % It is firstly shown that for all suitably regular initial data $(u_0, v_0, w_0)$, an associated Neumanntype initialboundary value problem possesses a globally defined bounded classical solution. Moreover, it is asserted that this solution stabilizes to a spatially homogeneous equilibrium at an exponential rate under a smallness condition on $\min\{\io u_0, \io v_0\}$ that appears to be consistent with predictions obtained from formal stability analysis.\abs
 Publication:

arXiv eprints
 Pub Date:
 February 2019
 DOI:
 10.48550/arXiv.1902.00848
 arXiv:
 arXiv:1902.00848
 Bibcode:
 2019arXiv190200848T
 Keywords:

 Mathematics  Analysis of PDEs
 EPrint:
 29 pages