Travelling front solutions arising in the chemotaxis-growth model
Using a singular limit procedure the authors study the dynamics of growth patterns in the bistable reaction-diffusion-advection system of biological species subjected to diffusion and chemotaxis \[ \frac{\partial u}{\partial t}=d_u\triangle u-\nabla (u\nabla\chi(v))+f(u),\; \frac{\partial v}{\partial t}=d_v\triangle v+\alpha u-\beta v,t>0,\;\chi\in \mathbb{R}^2. \] Here \(u(t,x)\) is their density and \(v(t,x)\) is the concentration of a chemical attractant, \(d_u\) and \(d_v\) are the diffusion rates of \(u\) and \(v\), \(\chi(v)\) is the chemostatic sensitivity function of the chemical attractant, \(\chi'(v)>0\) for \(v>0\). The dependence of pattern shapes on the measure \(k\) of the intensity of the chemotactic effect is also studied numerically.
scientific article; zbMATH DE number 5074419