Existence of positive travelling waves for generic Lotka-Volterra competition model with diffusion

Dynamics of Continuous, Discrete and Impulsive Systems Series B: Application and Algorithm

Volumn 6, Issue 3, 1999, Pages 345-365

  Kan On, Yukio ^a  

^a EHIME UNIVERSITY   (Japan)

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EID: 0011422715     PISSN: 14928760     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (11)

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2. C. Conley and R. Gardner, An application of the generalized Morse index to travelling wave solutions of a competitive reaction-diffusion model, Indiana Univ. Math. J., 33 (1984), pp. 319-343.
3. W. A. Coppel, Dichotomies in Stability Theory, Lecture Notes in Math. 629, Springer-Verlag, Berlin, 1978.
4. R. A. Gardner, Existence and stability of travelling wave solutions of competition models: A degree theoretic approach, J. Differential Equations, 44 (1982), pp. 343-364.
5. Y. Hosono, Singular perturbation analysis of travelling waves for diffusive Lotka-Volterra competition models, Numerical and applied mathematics, Part II (Paris, 1988), pp. 687-692.
6. Y. Kan-on and E. Yanagida, Existence of nonconstant stable equilibria in competition-diffusion equations, Hiroshima Math. J., 23 (1993), pp. 193-221.
7. Y. Kan-on, Parameter dependence of propagation speed of travelling waves for competition-diffusion equations, SIAM J. Math. Anal., 26 (1995), pp. 340-363.
8. Y. Kan-on, Fisher wave fronts for the Lotka-Volterra competition model with diffusion, Nonlinear Anal., 28 (1997), pp. 145-164.
9. H. Kokubu, Homoclinic and heteroclinic bifurcations of vector fields, Japan J. Appl. Math., 5 (1988), pp. 455-501.
10. M. Mimura and P. C. Fife, A 3-component system of competition and diffusion, Hiroshima Math. J., 16 (1986), pp. 189-207.
11. A. I. Vol'pert and V. A. Vol'pert, Application of the theory of the rotation of vector fields to the investigation of wave solutions of parabolic equations, Trans. Moscow Math. Soc., 1990, pp. 59-108.