density and is defined via a pressure law $p=P(n)$. This pressure exerted on cells induces a motion with a velocity field $v=v(x,t)$ related to the pressure through the Darcy’s law. The proliferation is modelled by a growth term $G(p)$ which is pressure dependent. With this assumption, the mathematical model reads $$\begin{aligned}
& \pa_t n + \nabla\cdot (n v) = n G(p),  \quad \mbox{ on }\ \RR^d\times\RR^+,  \\
& v = - \nabla p, \qquad p = P(n).\end{aligned}$$ In [@KimPozar; @MPQ; @PQTV; @PQV; @PV], the pressure law is given by $P(n)= \frac{\gamma}{\gamma -1}n^{\gamma-1}$ which allows to recover the porous medium equation. However, in many tissues, cells may not overlap, implying that the maximal packing density should be bounded by $1$. To take into account this non-overlapping constraint, the pressure law $P(n) = \epsilon \frac{n}{1-n}$ has been taken in [@HV]. This latter choice of pressure law has also been taken in the present paper. For this one population model, it has been showed in [@HV], that at the incompressible limit, $\epsilon \rightarrow 0$ (or $\gamma\to +\infty$ depending on the pressure expression), the model converges towards a Hele-Shaw type free boundary problem.

The previous model has the particularity to derive from the free 