Asymptotic stability in a chemotaxis-competition system with indirect signal production
نویسندگان
چکیده
This paper deals with a fully parabolic inter-species chemotaxis-competition system indirect signal production \begin{document}$ \begin{eqnarray*} \label{1a} \left\{ \begin{split}{} &u_{t} = \text{div}(d_{u}\nabla u+\chi u\nabla w)+\mu_{1}u(1-u-a_{1}v), &(x,t)\in \Omega\times (0,\infty), \\ &v_{t} d_{v}\Delta v+\mu_{2}v(1-v-a_{2}u), & w_{t} d_{w}\Delta w-\lambda w+\alpha v, \end{split} \right. \end{eqnarray*} $\end{document} under zero Neumann boundary conditions in smooth bounded domain $ \Omega\subset \mathbb{R}^{N} ($ N\geq 1 $), where d_{u}>0, d_{v}>0 and d_{w}>0 are the diffusion coefficients, \chi\in \mathbb{R} is chemotactic coefficient, \mu_{1}>0 \mu_{2}>0 population growth rates, a_{1}>0, a_{2}>0 denote strength coefficients of competition, \lambda \alpha describe rates degradation production, respectively. Global boundedness solutions to above \chi>0 was established by Tello Wrzosek [J. Math. Anal. Appl. 459 (2018) 1233-1250]. The main purpose further give long-time asymptotic behavior global solutions, which could not be derived previous work.
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ژورنال
عنوان ژورنال: Discrete and Continuous Dynamical Systems
سال: 2021
ISSN: ['1553-5231', '1078-0947']
DOI: https://doi.org/10.3934/dcds.2020315