Boundedness and stabilization in an indirect pursuit-evasion model with nonlinear signal-dependent diffusion and sensitivity

This paper deals with an indirect pursuit-evasion model with signal-dependent diffusion and sensitivity........... =. center dot (..1(..)...) -... center dot (..1(..).....) +.. (.... -.. 1 -.. 1..),.....,.. > 0,.... =. center dot (..2(..)...) +... center dot (..2(..).....) +.. (.. 2 -.. 2.. -..),.....,.. > 0,.... =.... +.... -....,.....,.. > 0,.... =.... +.... -....,.....,.. > 0, under homogeneous Neumann boundary conditions in a smoothly bounded domain... R2, where the parameters..,..,..,..,..,..,..,..1,..2,..1,.. 2 are positive,..1(..),..2(..) are signal-dependent diffusion coefficients,..1(..),..2(..) are nonlinear sensitivity functions. Firstly, using the energy estimate and Moser iteration, we demonstrate the existence of a unique globally bounded classical solution for the system. Furthermore, we investigate the asymptotic stabilization of globally bounded solutions. Finally, we provide numerical simulations that validate our theoretical findings.