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Some global dynamics of a Lotka-Volterra competition-diffusion-advection system

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  • This paper studies some population dynamics of a diffusive Lotka-Volterra competition advection model under no-flux boundary condition. We establish the main results that determine the stability of semi-trivial steady states.

    Mathematics Subject Classification: 35K51, 35K57, 35B09, 35B35, 92D25.

    Citation:

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  • [1] I. Averill, K. Y. Lam and Y. Lou, The role of advection in a two-species competition model: a bifurcation approach, Mem. Amer. Math. Soc., 245(1161) (2017). doi: 10.1090/memo/1161.
    [2] R. S. Cantrell and C. Cosner, Spatial Ecology Via Reaction-Diffusion Equations, Series in Mathematical and Computational Biology, Wiley, Chichester, UK, 2003. doi: 10.1002/0470871296.
    [3] R. S. CantrellC. Cosner and Y. Lou, Advection-mediated coexistence of competing species, Proc. R. Soc. Edinb. Sect. A, 137 (2007), 497-518.  doi: 10.1017/S0308210506000047.
    [4] X. F. ChenR. Hambrock and Y. Lou, Evolution of conditional dispersal:a reaction-diffusion-advection model, J. Math. Biol., 57 (2008), 361-386.  doi: 10.1007/s00285-008-0166-2.
    [5] C. Cosner, Reaction-diffusion-advection models for the effects and evolution of dispersal, Discrete Contin. Dyn. Syst., 34 (2014), 1701-1745.  doi: 10.3934/dcds.2014.34.1701.
    [6] R. Hambrock and Y. Lou, The evolution of conditional dispersal strategies in spatially heterogeneous habitats, Bull. Math. Biol., 71 (2009), 1793-1817.  doi: 10.1007/s11538-009-9425-7.
    [7] X. He and W. M. Ni, The effects of diffusion and spatial variation in Lotka-Volterra competition-diffusion system Ⅰ: heterogeneity vs. homogeneity, J. Differ. Equ., 254 (2013), 528-546.  doi: 10.1016/j.jde.2012.08.032.
    [8] X. He and W. M. Ni, The effects of diffusion and spatial variation in Lotka-Volterra competition-diffusion system Ⅱ: the general case, J. Differ. Equ., 254 (2013), 4088-4108.  doi: 10.1016/j.jde.2013.02.009.
    [9] X. He and W. M. Ni, Global dynamics of the Lotka-Volterra competition-diffusion system: diffusion and spatial heterogeneity Ⅰ, Commun. Pure Appl. Math., 69 (2016), 981-1014.  doi: 10.1002/cpa.21596.
    [10] X. He and W. M. Ni, Global dynamics of the Lotka-Volterra competition-diffusion system with equal amount of total resources Ⅱ, Calc. Var. Partial Differ. Equ., 55 (2016), 20. doi: 10.1007/s00526-016-0964-0.
    [11] X. He and W. M. Ni, Global dynamics of the Lotka-Volterra competition-diffusion system with equal amount of total resources Ⅲ, Calc. Var. Partial Differ. Equ., 56 (2017), 26. doi: 10.1007/s00526-017-1234-5.
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    [15] K. Y. Lam, Concentration phenomena of a semilinear elliptic equation with large advection in an ecological model, J. Differ. Equ., 250 (2011), 161-181.  doi: 10.1016/j.jde.2010.08.028.
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