Stability of monotone travelling waves for competition-diffusion equations
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- Kan-On, Y. & Fang, Q. Japan J. Indust. Appl. Math. (1996) 13: 343. doi:10.1007/BF03167252
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We consider the Lotka-Volterra competition model with diffusion inR, and establish a theorem on the asymptotic stability of monotone travelling waves relative to the space of bounded uniformly continuous functions with the supremum norm. In consideration of the result of Alexander et al.  and Derndinger , we shall arrive at a study of the non-negative eigenvalues of the linearized operator around the travelling wave.