  We study the Universe at the late stage of its evolution and deep inside the
cell of uniformity. At such a scale the Universe is highly inhomogeneous and
filled with discretely distributed inhomogeneities in the form of galaxies and
groups of galaxies. As a matter source, we consider dark matter (DM) and dark
energy (DE) with a non-linear interaction $Q = 3\mathcal{H}\gamma
\bar\varepsilon_{\mathrm{DE}} \bar\varepsilon_{\mathrm{DM}} /
(\bar\varepsilon_{\mathrm{DE}} + \bar\varepsilon_{\mathrm{DM}})$, where
$\gamma$ is a constant. We assume that DM is pressureless and DE has a constant
equation of state parameter $w$. In the considered model, the energy densities
of the dark sector components present a scaling behaviour with
$\bar\varepsilon_{\mathrm{DM}} / \bar\varepsilon_{\mathrm{DE}} \sim \left({a_0}
/ {a} \right)^{-3(w+\gamma)}$. We investigate the possibility that the
perturbations of DM and DE, which are interacting among themselves, could be
coupled to the galaxies with the former being concentrated around them. To
carry our analysis, we consider the theory of scalar perturbations (within the
mechanical approach), and obtain the sets of parameters $(w,\gamma)$ which do
not contradict it. We conclude that two sets: $(w=-2/3,\gamma=1/3)$ and
$(w=-1,\gamma=1/3)$ are of special interest. First, the energy densities of DM
and DE on these cases are concentrated around galaxies confirming that they are
coupled fluids. Second, we show that for both of them, the coincidence problem
is less severe than in the standard $\Lambda$CDM. Third, the set
$(w=-1,\gamma=1/3)$ is within the observational constraints. Finally, we also
obtain an expression for the gravitational potential in the considered model.
