Year: 2019
Type: preprint
Abstract: \begin{abstract} \noindent % We consider the one-dimensional parabolic system The system \bas \left\{ \begin{array}{l} u_t= u_{xx} - χ_1 (uw_x)_x, \\[1mm] v_t = v_{xx} - χ_2 (vu_x)_x, \\[1mm] w_t = dw_{xx} - λ(u+v)w - μw + r, \end{array} \right. \eas % that has been proposed as a model to describe social interactions within mixed forager-exploiter groups. is considered in a bounded real interval, with positive parameters $χ_1,χ_2,d,λ$ and $μ$, and with $r \ge 0$. Proposed to describe social interactions within mixed forager-exploiter groups, this model extends classical one-species chemotaxis-consumption 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 Neumann-type initial-boundary 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
Source: arXiv (Cornell University)
Authors: Tao, Youshan, Winkler, Michael
Institutions: Donghua University, Paderborn University
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2912413091