Dynamics of spike in a Keller-Segel's minimal chemotaxis model
Dynamics of spike in a Keller-Segel's minimal chemotaxis model
The dynamics are studied for the Keller-Segel's minimal chemotaxis model $τ u_t=(u_x-kuv_x)_x, \ \ \ \ v_t=v_{xx}-v+u$ on a bounded interval with homogeneous Neumann boundary conditions, where $\tau\geqslant 0$ and $k\gg 1$ are parameters and the total mass of $u$ is scaled to be one. In general, the dynamics can …