We investigate the spreading properties of a three-species competition-diffusion system, which is non-cooperative. We apply the Hamilton-Jacobi approach, due to Freidlin, Evans and Souganidis, to establish upper and lower estimates of spreading speed of the slowest species, in terms of the spreading speed of two faster species, and show that the estimates are sharp in some situations. The spreading speed will first be characterized as the free boundary point of the viscosity solution for certain variational inequality cast in the space of speeds. Its exact formulas will then be derived by solving the variational inequality explicitly. To the best of our knowledge, this is the first theoretical result on three-species competition system in unbounded domains.

中文翻译：

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具有三个物种的竞争扩散模型中的堆叠入侵波

我们研究了非合作的三物种竞争扩散系统的传播特性。由于 Freidlin、Evans 和 Souganidis，我们应用 Hamilton-Jacobi 方法，根据两个较快物种的传播速度建立最慢物种传播速度的上限和下限估计，并表明估计在某些情况下是尖锐的情况。传播速度首先被表征为速度空间中某些变分不等式的粘度解的自由边界点。然后将通过显式求解变分不等式推导出其精确公式。据我们所知，这是无界域中三物种竞争系统的第一个理论成果。