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In this paper, we investigate a diffusive Lotka-Volterra predator-prey model with nonlinear prey-taxis under Neumann boundary conditions. This system describes a prey-taxis mechanism that is an immediate movement of the predator u in response to a change of the prey v (which lead to the collection of u). We apply some methods to overcome the substantial difficulty of the existence of nonlinear prey-taxis term and prove that the unique global classical solutions of Lotka-Volterra predator-prey model are globally bounded.

Global existence and boundedness of solutions in a Lotka-Volterra reaction-diffusion system of predator-prey model with nonlinear prey-taxis