Global existence of solutions to a cross-diffusion predator–prey system with Holling type-II functional response

This paper is concerned with a cross-diffusion system arising in a predator–prey population model with Holling type-II functional response in a bounded domain with no flux boundary condition. Employing the energy estimates and Gagliardo–Nirenberg type inequalities to establish W21-bounds uniform in time, the global existence and uniform boundedness of solutions for a cross-diffusion system are proved. The global asymptotic stability of the constant positive steady state is also investigated.