Global existence and uniqueness of solutions in a chemotaxis system with density-suppressed motility, a $θ-$logistic source, and indirect signal production under a strong Allee effect

We consider the following chemotaxis-growth system, featuring density-suppressed motility and a $θ$-logistic growth term that incorporates a strong Allee effect: \begin{equation*} \left\{ \begin{aligned} u_t &= Δ(γ(v)u) + μu(1-u^θ)(u-A), & x \in Ω, \quad t > 0, v_t &= Δv - v+ w^β, & x \in