一类浮游生物植化相克抛物方程

A parabolic equation of plankton allelopathy

研究2种群竞争抑制系统,利用上下解的方法给出了抛物方程组解的存在性和惟一性的证明,讨论对应常微分方程组平衡解的全局稳定性,给出相应椭圆系统的Harnack不等式,并通过构造Lyapunov泛函说明在种群内部竞争激烈或扩散系数足够大的条件下,其对应的椭圆系统没有非常数解.

In this paper, the two-species competition-retrains system is studied. Making use of upper and lower solutions, this text proves the exsistence and uniqueness of the parabolic equations. Equilibrium solutions of the ODE system are discussed, and the Harnack inequality of the elliptic system is given. By the method of constructing the Lyapunov functional, it is shown that there are no non-constant solutions to the elliptic problem if inter-specific competitions are strong or if the diffusion rates of species are high enough.