Boundedness and asymptotic behavior in a predator-prey model with indirect pursuit-evasion interaction

Abstract

<p style='text-indent:20px;'>In this paper, we study the prey-predator model with indirect pursuit-evasion interaction defined on a smooth bounded domain with homogeneous Neumann boundary conditions. We obtain the globa existence and boundedness of the classical solution of the model by estimating <inline-formula><tex-math id="M1">\begin{document}$ L^{p} $\end{document}</tex-math></inline-formula>-norm of <inline-formula><tex-math id="M2">\begin{document}$ u $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M3">\begin{document}$ v $\end{document}</tex-math></inline-formula>, and we also show the large time behavior and convergence rate of the solution.</p>