| Abstract: |
| The interactions between diffusion and spatial heterogeneity could create interesting dynamics for a spatial population model. We show that for two-component Lotka-Volterra competition model with spatially heterogeneous diffusion coefficients, intrinsic growth rates and competition rates, a spatially heterogeneous positive equilibrium solution is globally asymptotically stable when it exists. A similar result is also proved for multi-component Lotka-Volterra competition model with spatially heterogeneous intrinsic growth rates. We prove the result by using monotone dynamical theory, upper and lower solution methods, and a new Lyapunov functional method. |
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