Uniqueness and large-time continuous dependence in a doubly degenerate nutrient taxis system

\[ u_t = \nabla \cdot (uv\nabla u) - χ\nabla\cdot (u^2 v\nabla v) + \ell uv, \qquad \qquad v_t = Δv - uv, \] is considered in a smoothly bounded domain $Ω\subset {\mathbb{R}}^n$ and with $χ\ge 0$ and $\ell\ge 0$. Within a suitable concept of solvability, a statement on uniqueness of solution