Abstract：
This paper aims to establish the existence of traveling wave solutions connecting different equilibria for a spatial eco-epidemiological predator-prey system in advective environments. After applying the traveling wave coordinates, these solutions correspond to heteroclinic orbits in phase space. We investigate the existence of the traveling wave solution connecting from a boundary equilibrium to a co-existence equilibrium by using a shooting method. Different from the techniques introduced by Huang, we directly prove the convergence of the solution to a co-existence equilibrium by constructing a special bounded set. Furthermore, the Lyapunov-type function we constructed does not need the condition of bounded below. Our approach provides a different way to study the existence of traveling wave solutions about the co-existence equilibrium. The existence of traveling wave solutions between co-existence equilibria are proved by utilizing the qualitative theory and the geometric singular perturbation theory. Some other open questions of interest are also discussed in the paper.
摘要：
本文旨在建立平流环境中空间生态流行病学捕食者-食饵系统连接不同均衡的行波解的存在性。应用行波坐标后，这些解对应于相空间中的异斜轨道。我们使用射击方法研究了从边界平衡到共存平衡的行波解的存在性。与黄介绍的技术不同，我们通过构造一个特殊的有界集，直接证明了解对共存均衡的收敛性。此外，我们构造的Lyapunov型函数不需要下面的有界条件。我们的方法提供了一种不同的方法来研究关于共存平衡的行波解的存在性。利用定性理论和几何奇异摄动理论证明了共存均衡之间行波解的存在性。本文还讨论了其他一些感兴趣的悬而未决的问题。
