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 \overline { \varepsilon } _ { \mathrm { DE } } \overline { \varepsilon } % _ { \mathrm { DM } } / ( \overline { \varepsilon } _ { \mathrm { DE } } + \overline { \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 \overline { \varepsilon } _ { \mathrm { DM } } / \overline { \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 .