Global Solvability for a Predator-Prey Model with Prey-Taxis and Rotational Flux Terms

Abstract

In this paper the author investigates the following predator-prey model with prey-taxis and rotational flux terms $\left\{ {\matrix{{{u_t} = \Delta u - \nabla \cdot (uS(x,u,v)\nabla v) + \gamma uF(v) - uh(u),} \hfill & {x \in \Omega ,\,\,\,\,\,t > 0,} \hfill \cr {{v_t} = D\Delta v - uF(v) + f(v),} \hfill & {x \in \Omega ,\,\,\,\,\,t > 0} \hfill \cr } } \right.\,\,\,\,( * )$

in a bounded domain with smooth boundary. He presents the global existence of generalized solutions to the model (*) in any dimension.

Keywords

Predator-prey / Prey-taxis / Global existence / Rotational flux