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New finite element methods are proposed for elliptic interface problems in one and two dimensions. The main motivation is to get not only an accurate solution, but also an accurate first order derivative at the interface (from each side). The key in 1D is to use the idea of Wheeler (1974). For 2D interface problems, the point is to introduce a small tube near the interface and propose the gradient...
This paper studies the dynamics of a chemostat model with n populations competing for one nutrient which can be recycled due to decomposition of dead biomass. Several kinds of results about local and global stability of non-negative equilibria, uniform persistence and control of populations are obtained.
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