The minimal wave speed to the Lotka-Volterra competition model. (English) Zbl 1436.35064
Summary: This paper focuses on selection mechanisms of the minimal speed of traveling waves to the Lotka-Volterra reaction-diffusion model. We first establish general conditions for the linear and nonlinear selection by way of an upper and lower solution method. Then some explicit criteria are derived by subtly constructing formulas of upper and lower solutions. The obtained conditions substantially improve or complement the corresponding results in the known references.
MSC:
| 35C07 | Traveling wave solutions |
| 35K57 | Reaction-diffusion equations |
| 92D25 | Population dynamics (general) |
Keywords:
linear selection; nonlinear selection; Lotka-Volterra model; upper and lower solution methodReferences:
| [1] | Alhasanat, A.; Ou, C., On a conjecture raised by Yuzo Hosono, J. Dyn. Differ. Equ., 31, 287-304 (2019) · Zbl 1408.35068 |
| [2] | Alhasanat, A.; Ou, C., Minimal-speed selection of traveling waves to the Lotka-Volterra competition model, J. Differ. Equ., 266, 7357-7378 (2019) · Zbl 1408.35067 |
| [3] | Kan-on, Y., Fisher wave fronts for the Lotka-Volterra competition model with diffusion, Nonlinear Anal., 28, 145-164 (1997) · Zbl 0868.35053 |
| [4] | Li, B.; Weinberger, H. F.; Lewis, M. A., Spreading speeds as slowest wave speeds for cooperative systems, Math. Biosci., 196, 82-98 (2005) · Zbl 1075.92043 |
| [5] | Liang, X.; Zhao, X-Q., Asymptotic speed of spread and traveling waves for monotone semiflows with applications, Commun. Pure Appl. Math., 60, 1-40 (2007) · Zbl 1106.76008 |
| [6] | Ma, M.; Ou, C., Linear and nonlinear speed selection for mono-stable wave propagations, SIAM J. Math. Anal., 51, 1, 321-345 (2019) · Zbl 1407.35114 |
| [7] | Okubo, A.; Maini, P. K.; Williamson, M. H.; Murray, J. D., On the spatial spread of the grey squirrel in Britain, Proc. R. Soc. Lond. B, Biol. Sci., 238, 113-125 (1989) |
| [8] | Volpert, A. I.; Volpert, Vi. A.; Volpert, Vl., Traveling Wave Solutions of Parabolic Systems, Translations of Mathematical Monographs, vol. 140 (1994), American Mathematical Society · Zbl 0805.35143 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
