  Global existence of very weak solutions to a non-local
diffusion-advection-reaction equation is established under no-flux boundary
conditions in higher dimensions. The equation features degenerate myopic
diffusion and nonlocal adhesion and is an extension of a mass-conserving model
recently derived in arXiv:2308.05676. The admissible degeneracy of the
diffusion tensor is characterised in terms of the upper box fractal dimension.
