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摘要
This paper studies the predator-prey systems with prey-taxis @@@ {u(t) = Delta u-chi del . (u del v) + gamma uv - rho u, @@@ v(t) = Delta v - xi uv + mu v(1 - v), @@@ in a bounded domain Omega subset of R-n (n = 2, 3) with Neumann boundary conditions, where the parameters chi, gamma, rho, xi and mu are positive. It is shown that the two-dimensional system possesses a unique global-bounded classical solution. Furthermore, we use some higher-order estimates to obtain the classical solu-tions with uniform-in-time bounded for suitably small initial data. Finally, we establish that the solution stabilizes towards the prey-only steady state (0, 1) if rho > gamma and towards the co-existence steady state (mu(gamma-rho)/xi rho, rho/gamma) if gamma > rho under some conditions in the norm of L-infinity(Omega) as t -> infinity.
