Journal of Differential Equations
This paper proves the global existence and boundedness of solutions to a general reaction diffusion predator prey system with prey-taxis defined on a smooth bounded domain with no-flux boundary condition. The result holds for domains in arbitrary spatial dimension and small prey-taxis sensitivity coefficient. This paper also proves the existence of a global attractor and the uniform persistence of the system under some additional conditions. Applications to models from ecology and chemotaxis are discussed. (C) 2016 Elsevier Inc. All rights reserved.
Wu, S., Shi, J., & Wu, B. (2016). Global existence of solutions and uniform persistence of a diffusive predator–prey model with prey-taxis. Journal of Differential Equations, 260(7), 5847-5874.