AI 中文总结
本文通过几何奇异摄动理论，证明了两物种Lotka-Volterra竞争-扩散系统中连接共存态与平凡态的行波存在性，并分析了其单调性与渐近稳定性。
AI 中文摘要
我们考虑两物种Lotka-Volterra竞争-扩散系统，其中一个物种相对于另一物种具有较小的扩散速率和较小的竞争系数。通过几何奇异摄动理论，我们证明了连接共存态到平凡态的波前解的存在性，其传播速度大于最小速度。对于此类波前解，我们证明了两物种的轮廓均为单调的。最后，我们利用几何奇异摄动理论估计相关的Evans函数，并给出相应的稳定性结果。
英文摘要
We consider the two-species Lotka-Volterra competition-diffusion system where one species has a small diffusion rate relative to the other species and has a small competition coefficient. By the geometric singular perturbation theory, we prove the existence of the wavefront connecting the coexistence state to the trivial state, with traveling speed greater than the minimal speed. For such wavefronts, we show that the profiles of both species are monotone. Finally, we use the geometric singular perturbation theory to estimate the associated Evans function, and give the related stability results.
Comments24 pages, 4 figures
