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

We study a chemotaxis system on bounded domain in two dimensions where the formation of chemical potential is subject to the Dirichlet boundary condition. 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 8π 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.