On a repulsion-diffusion equation with immigration.

We study a repulsion-diffusion equation with immigration and linear diffusion, whose asymptotic behaviour is related to stability of long-term dynamics in spatial population models and other branching particle systems. We prove well-posedness and find sharp conditions on the repulsion under which a form of the maximum principle and a strong notion of global boundedness of solutions hold. The critical asymptotic strength of the repulsion is $ |x|^{1-d} $, that of the Newtonian potential. [ABSTRACT FROM AUTHOR]