Convergence of global and bounded solutions of a two-species chemotaxis model with a logistic source

By Ke Lin, Chunlai Mu. 2017

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In this paper, we consider a system of three parabolic equations in high-dimensional smoothly bounded domain \begin{document}$\left\{\begin{array}{llll}u_t=\Delta u-\chi_1\nabla\cdot( u\nabla w)+\mu_1u(1-u-a_1v),\quad x'>which describes the mutual competition between two populations on account of the Lotka-Volterra dynamics. For any cross-diffusivities $\chi_1>0$ and $\chi_2>0$ and the rates $a_1>0$ and $a_2>0$, it is proved that the global classical bounded solutions exist for sufficiently regular initial data when the parameters $\mu_1$ and $\mu_2$ are sufficiently large. In deriving the convergence of solutions to this system, we need to distinguish two cases $a_1, a_2\in[0, 1)$ and $a_1>1$ and $0\leq a_2

Subfields: Modeling and Simulation, Molecular Biology, Public Health, Environmental and Occupational Health

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