On kinetic and macroscopic models for the stripe formation in engineered bacterial populations

作者：Jiang, Ning; Liang, Jiangyan^*; Luo, Yi-Long; Tang, Min; Zhang, Yaming

来源：Journal of Differential Equations, 2022, 323: 38-85.

DOI：10.1016/j.jde.2022.03.035

• K-EECP and AD-EECP model
• Positivity
• Conservation laws
• Density-dependent mobility
• z-flux term
• Nonlinearity of diffusion structure

We study the well-posedness of the biological models with AHL-dependent cell mobility on engineered Escherichia coli populations. For the kinetic model proposed by Xue-Xue-Tang recently [17], the local existence for large initial data is proved first. Furthermore, the positivity and local conservation laws for density and nutrient concentration with initial assumptions (1.24) and (1.26) are justified. Based on these properties, it can be extended globally in time near the equilibrium (0, 0, 0). Considering the asymptotic behaviors of faster response CheZ turnover rate, one formally derives an anisotropic diffusion engineered Escherichia coli populations model (in short, AD-EECP) for which we find a key extra a priori estimate to overcome the difficulties coming from the nonlinearity of the diffusion structure. The local well-posedness and the positivity and local conservation laws for density and nutrient of the AD-EECP are justified. Furthermore, the global existence around the stable steady-state is obtained.

• 单位
  上海交通大学; 武汉大学