  This paper is devoted to the analysis of non-negative solutions for a
generalisation of the parabolic equation with porous medium like nonlinear
diffusion and nonlinear nonlocal reaction. We investigate under which
conditions equilibration between two competing effects, repulsion modelled by
nonlinear diffusion and aggregation modelled by nonlinear reaction, occurs.
Precisely, we exhibit that the qualitative behavior of solutions is decided by
the nonlinear diffusion which is chosen in such a way that its scaling and the
reaction term coincide, i.e. that there is a critical exponent $m+2/n$ for the
reaction exponent $\alpha,$ solutions exist globally with uniformly upper
bounds in the case of (i)$1\le \alpha<m+2/n$ for any initial data, (ii)
$\alpha>m+2/n$ for small initial data and (iii) $\alpha=m+2/n$ for small mass
capacity $M_0$. In the case of (ii) and (iii), the decay properties of the
solution are also discussed. Moreover, numerical simulations are carried out to
verify the theoretical analysis and explore other issues that lie beyond the
scope of the analysis.
