Classical solutions to a pursuit‐evasion model with prey‐taxis and indirect predator‐taxis

Abstract

This paper investigates a pursuit‐evasion model with prey‐taxis and indirect predator‐taxis in a bounded domain with homogeneous Neumann boundary conditions, where and for . We prove the global boundedness of classical solution of ( ) under is suitably small and other conditions. Moreover, we also show the long‐time asymptotic behavior and convergence rate of the solution.