Global existence of solutions and uniform persistence of a diffusive predator-prey model with prey-taxis ✩

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Global dynamics and spatio-temporal patterns of predator–prey systems with density-dependent motion (2019, background): “[2, 6, 23, 24, 37, 46]), and in particular the global existence and stability of solutions have been established in a previous work by the authors in [13].”
Depleting the signal: Analysis of chemotaxis‐consumption models—A survey (2023, background): “Precedents and close relatives concerned with questions of global solvability, boundedness and spatially homogeneous asymptotics in (CC7) and neighboring systems can be found in [103], [44], [153], [155], [117], [53], [71], [113] and [144], and an impression about the numerous recent developments in”
Global stability of prey-taxis systems (2017, unknown): “6) with χ > 0 small was obtained under the condition F(v) ≤ C for some constant C > 0 (see hypothesis (H ∗ 2 ) in [46]) in any dimension.”
Large time behavior in a predator-prey system with indirect pursuit-evasion interaction (2017, background): “also [28], [12], [8], [16], [19], [29] and [21] for some closely related variants).”