具渗流扩散和间接信号产生的Prey-Taxis模型解的整体存在性与稳定性

Global Existence and Stability to a Prey-Taxis Model with Porous Medium Diffusion and Indirect Signal Production

该文考虑如下prey-taxis模型■在三维有界区域上的零流边值问题.该文证明了对任意的m1>1,m2>1,对任意大的初值,模型存在一个全局弱解.并在一致有界性的基础上,研究了解的大时间行为,建立了定常状态的全局渐近稳定性理论.确切地说,该文证明了当λ=0,α≥0时,全局弱解强收敛到(u0,0,0);当λ≥0,α=0时,如果λ<F0(u),全局弱解强收敛到(u0,0,0),如果λ>F0(u),全局弱解强收敛到(u0,0,k(1-F0(u)/λ)).

In this pap er,we consider the following prey-taxis mo del with nonlinear di usion and indirect signal pro duction ■in a b ounded domain of R^3 withzero-ux b oundary condition.It is shown that for any m1>1,m2>1,there exists a global b ounded weak solution for any large initial datum.Based on the uniform b oundedness prop erty,we also studied the large time b ehavior of solutions,and the global asymptotically stability of the constant steady states are established.More precisely,we showed that when λ=0,α≥0,the global weak solution converges to(u0,0,0)in the large time limit;whenλ>0,α=0,the global weak solution converges to(u0,0,0)ifλ<F0(u),and the global weak solution converges to(u0,0,k(1-F0(u)/λ))if λ>F0(u).