竞争-竞争-互惠交错扩散模型的整体解

The Global Solution for the Competitor-Competitor-Mutualist Model with Cross-Diffusion

竞争-竞争-互惠交错扩散模型是一类强耦合的抛物型方程组,关于该模型时变解的整体存在性的研究结果很少,特别是在高维空间中。本文应用能量估计方法,极值原理和抛物型方程的正则性理论证明了:对竞争种群含弱交错扩散项的竞争-竞争-互惠交错扩散模型,它在任意维空间中存在古典的整体解。

The competitor-competitor-mutualist model with cross-diffusion is a strongly-coupled parabolic system. There are few results about the global existence of time-dependent solutions of this model, especially in higher dimensions space. In this paper, by using the energy estimate method, the maximum principle and the regularity of parabolic equations, we prove the global existence of classical solutions in any dimensional space for the competitor-competitor-mutualist model with weak cross-diffusion in the competitive species.