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The sign of the wave speed for the Lotka-Volterra competition-diffusion system
1. | Department of Mathematics, Tamkang University, 151, Ying-Chuan Road, Tamsui, Taipei County 25137 |
2. | Department of Mathematics, National Taiwan Normal University, 88, S-4, Ting Chou Road, Taipei 11677 |
References:
[1] |
C. Conley and R. Gardner, An application of the generalized Morse index to travelling wave solutions of a competitve reaction-diffusion model, Indiana Univ. Math. J., 33 (1984), 319-343. |
[2] |
R. A. Gardner, Existence and stability of traveling wave solutions of competition models: A degree theoretic approach, J. Differential Equations, 44 (1982), 343-364.
doi: 10.1016/0022-0396(82)90001-8. |
[3] |
J.-S. Guo and X. Liang, The minimal speed of traveling fronts for the Lotka-Volterra competition system, J. Dyn. Diff. Equat., 23 (2011), 353-363.
doi: 10.1007/s10884-011-9214-5. |
[4] |
Y. Hosono, The minimal speed of traveling fronts for a diffusive Lotka-Volterra competition model, Bulletin of Math. Biology, 60 (1998), 435-448.
doi: 10.1006/bulm.1997.0008. |
[5] |
Y. Kan-on, Parameter dependence of propagation speed of travelling waves for competition-diffusion equations, IAM J. Math. Anal., 26 (1995), 340-363.
doi: 10.1137/S0036141093244556. |
[6] |
Y. Kan-on, Existence of standing waves for competition-diffusion equations, Japan J. Indust. Appl. Math., 13 (1996), 117-133.
doi: 10.1007/BF03167302. |
[7] |
Y. Kan-on, Stability of monotone travelling waves for competition-diffusion equations, Japan J. Indust. Appl. Math., 13 (1996), 343-349.
doi: 10.1007/BF03167252. |
[8] |
Y. Kan-on, Fisher wave fronts for the Lotka-Volterra competition model with diffusion, Nonlinear Analysis, TMA, 28 (1997), 145-164.
doi: 10.1016/0362-546X(95)00142-I. |
[9] |
Y. Kan-on and E. Yanagida, Existence of nonconstant stable equilibria in competition-diffusion equations, Hiroshima Math. J., 23 (1993), 193-221. |
[10] |
M. Mimura and P. C. Fife, A 3-component system of competition and diffusion, Hiroshima Math. J., 16 (1986), 189-207. |
[11] |
M. Rodrigo and M. Mimura, Exact solutions of a competition-diffusion system, Hiroshima Math. J., 30 (2000), 257-270. |
[12] |
M. M. Tang and P. C. Fife, Propagating fronts for competing species equations with diffusion, Arch. Rational Mech. Anal., 73 (1980), 69-77.
doi: 10.1007/BF00283257. |
show all references
References:
[1] |
C. Conley and R. Gardner, An application of the generalized Morse index to travelling wave solutions of a competitve reaction-diffusion model, Indiana Univ. Math. J., 33 (1984), 319-343. |
[2] |
R. A. Gardner, Existence and stability of traveling wave solutions of competition models: A degree theoretic approach, J. Differential Equations, 44 (1982), 343-364.
doi: 10.1016/0022-0396(82)90001-8. |
[3] |
J.-S. Guo and X. Liang, The minimal speed of traveling fronts for the Lotka-Volterra competition system, J. Dyn. Diff. Equat., 23 (2011), 353-363.
doi: 10.1007/s10884-011-9214-5. |
[4] |
Y. Hosono, The minimal speed of traveling fronts for a diffusive Lotka-Volterra competition model, Bulletin of Math. Biology, 60 (1998), 435-448.
doi: 10.1006/bulm.1997.0008. |
[5] |
Y. Kan-on, Parameter dependence of propagation speed of travelling waves for competition-diffusion equations, IAM J. Math. Anal., 26 (1995), 340-363.
doi: 10.1137/S0036141093244556. |
[6] |
Y. Kan-on, Existence of standing waves for competition-diffusion equations, Japan J. Indust. Appl. Math., 13 (1996), 117-133.
doi: 10.1007/BF03167302. |
[7] |
Y. Kan-on, Stability of monotone travelling waves for competition-diffusion equations, Japan J. Indust. Appl. Math., 13 (1996), 343-349.
doi: 10.1007/BF03167252. |
[8] |
Y. Kan-on, Fisher wave fronts for the Lotka-Volterra competition model with diffusion, Nonlinear Analysis, TMA, 28 (1997), 145-164.
doi: 10.1016/0362-546X(95)00142-I. |
[9] |
Y. Kan-on and E. Yanagida, Existence of nonconstant stable equilibria in competition-diffusion equations, Hiroshima Math. J., 23 (1993), 193-221. |
[10] |
M. Mimura and P. C. Fife, A 3-component system of competition and diffusion, Hiroshima Math. J., 16 (1986), 189-207. |
[11] |
M. Rodrigo and M. Mimura, Exact solutions of a competition-diffusion system, Hiroshima Math. J., 30 (2000), 257-270. |
[12] |
M. M. Tang and P. C. Fife, Propagating fronts for competing species equations with diffusion, Arch. Rational Mech. Anal., 73 (1980), 69-77.
doi: 10.1007/BF00283257. |
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