On the finite-time blow-up of a non-local parabolic equation describing chemotaxis
On the finite-time blow-up of a non-local parabolic equation describing chemotaxis
The non-local parabolic equation \[ v_t=\Delta v+\frac{\lambda e^v}{\int_\Omega e^v}\quad\mbox{in $\Omega\times (0,T)$} \] associated with Dirichlet boundary and initial conditions is considered here. This equation is a simplified version of the full chemotaxis system. Let $\lambda^*$ be such that the corresponding steady-state problem has no solutions for $\lambda>\lambda^*$, then it is …