Global existence and asymptotic stability in a competitive twospecies chemotaxis system with two signals
Tobias Black  Institut für Mathematik, Universität Paderborn, Warburger Str. 100, 33098 Paderborn, Germany (email) Abstract:
We consider the twospeciestwochemical chemotaxis system
\begin{align*}
\left\{\begin{array}{r@{\,}l@{\quad}l@{\,}c}
u_{t}\ &=\Delta u\chi_1\nabla\!\cdot(u\nabla v)+\mu_1 u(1ua_1w),\ &x\in\Omega,& t>0,\\
v_{t}\ &=\Delta vv+w,\ &x\in\Omega,& t>0,\\
w_{t}\ &=\Delta w\chi_2\nabla\!\cdot(w\nabla z)+\mu_2 w(1wa_2u),\ &x\in\Omega,& t>0,\\
z_{t}\ &=\Delta zz+u,\ &x\in\Omega,& t>0,\\
\end{array}\right.
\end{align*}
where $\Omega\subset\mathbb{R}^n$ is a bounded domain with smooth boundary.
The system models LotkaVolterra competition of two species coupled with an additional chemotactic influence. In this model each species is attracted by the signal produced by the other.
Keywords: Multispecies chemotaxis, boundedness, logistic source, LotkaVolterra competition, stability.
Received: June 2016; Revised: June 2016; Available Online: February 2017. 
2016 Impact Factor.994
