Global solvability in a Keller-Segel-growth system with indirect signal production
The author studies a chemotaxis model with indirect signal production and reaction term \[ u_t=\Delta u-\chi\nabla\cdot(u\nabla v)+f(u), \] \[ \tau v_t=\Delta v-v+w, \] \[ \tau w_t=\Delta w-w+u, \] in bounded domains of \(\mathbb R^N\), with the homogeneous Neumann boundary conditions. Under the assumption \(\frac{f(s)}{s}\to-\infty\) as \(s\to\infty\) and \(f(0)\ge 0\), suitable generalized solutions are shown to to global-in-time. For a a generalized logistic term \(f(s)=\lambda s-\mu s^\kappa\) similar results are shown for \(\kappa \ge 2-\frac2N\) if \(N\ge 3\), and \(\kappa>1\) if \(N=2\).
scientific article; zbMATH DE number 7597567
scientific article