The purpose of this work is to investigate the existence and stability of monostable traveling wavefronts for a Lotka–Volterra competition model with partially nonlocal interactions. We first establish an innovative lemma for the existence of positive solutions to a system of linear inequalities. By this lemma, we can construct a pair of sub-super-solutions and derive the existence result by applying the technique of monotone iteration method. It is found that if the ratio of the diffusive rate of the species without nonlocal interactions to that of the other species is not greater than a specific value, then the minimal wave speed of the wavefronts is linearly determined. Moreover, by the spectral analysis of the linearized operators, we show that the traveling wavefronts are essentially unstable in the space of uniformly continuous functions. However, if the initial perturbations of the traveling wavefronts belong to certain exponential weighted spaces, then we prove that the traveling wavefronts with noncritical wave speed are asymptotically stable in the exponential weighted spaces.

这项工作的目的是研究具有部分非局部相互作用的Lotka-Volterra竞争模型的单稳态行波前波的存在和稳定性。我们首先为线性不等式系统的正解的存在建立一个创新的引理。通过这个引理，我们可以构造一对子超解，并通过应用单调迭代法的技术得出存在结果。已经发现，如果没有非局部相互作用的物质的扩散速率与其他物质的扩散速率之比不大于特定值，则线性确定波前的最小波速。此外，通过线性化算子的频谱分析，我们表明行波波前在均匀连续函数空间中基本上是不稳定的。