Abstract
A spatially discrete version of the diffusive Lotka-Volterra equations is considered. Asymptotical spatial homogeneity of solutions of the equations with equilibrium, periodic or zero flux boundary conditions is proved without regard to crowding effects. The proof does not require the assumption of equal diffusion coefficients and the restrictions on the dimension of space and on the initial data, which are necessary in the spatially continuous model.
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Namba, T. Asymptotic behaviour of solutions of the diffusive Lotka-Volterra equations. J. Math. Biology 10, 295–303 (1980). https://doi.org/10.1007/BF00276988
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DOI: https://doi.org/10.1007/BF00276988