Nonlinear stability of chemotactic clustering with discontinuous advection
Nonlinear stability of chemotactic clustering with discontinuous advection
We perform the nonlinear stability analysis of a one-dimensional chemotaxis model of bacterial self-organization, assuming that bacteria respond sharply to chemical signals. The resulting discontinuous advection speed represents the key challenge for the stability analysis. We follow a perturbative approach, where the shape of the cellular profile is clearly separated …