Abstract
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.
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The authors would like to thank the anonymous referees for their valuable comments and suggestions which have led to an improvement of the presentation.
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C.-H. Chang: Partially supported by the MOST of Taiwan. C.-H. Hsu: Partially supported by the MOST and NCTS of Taiwan. T.-S. Yang: Partially supported by the MOST of Taiwan.
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Chang, CH., Hsu, CH. & Yang, TS. Traveling wavefronts for a Lotka–Volterra competition model with partially nonlocal interactions. Z. Angew. Math. Phys. 71, 70 (2020). https://doi.org/10.1007/s00033-020-1289-6
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DOI: https://doi.org/10.1007/s00033-020-1289-6
Keywords
- Super- and subsolutions
- Essential spectrum
- Normal spectrum
- Monotone system
- Exponential weighted space
- Positive solutions of linear inequalities