Exclusion of boundary blowup for a 2D chemotaxis system provided with Dirichlet boundary condition for the Poisson part

We study a chemotaxis system on a bounded domain in two dimensions where the formation of the chemical potential is subject to Dirichlet boundary conditions. For such a system the solution is kept bounded near the boundary and hence the blowup set is composed of a finite number of interior points. If the initial total mass is 8 $\pi$ and the domain is close to a disc then the solution exhibits a collapse in infinite time of which movement is subject to a gradient flow associated with the Robin function.