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# A competition-diffusion system approximation to the classical two-phase Stefan problem

(Impact Factor: 0.27). 06/2001; 18(2):161-180. DOI: 10.1007/BF03168569

ABSTRACT A new type of competition-diffusion system with a small parameter is proposed. By singular limit analysis, it is shown that
any solution of this system converges to the weak solution of the two-phase Stefan problem with reaction terms. This result
exhibits the relation between an ecological population model and water-ice solidification problems.

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ABSTRACT: In this paper we study two kinds of free boundary problems for the diffusive prey–predator model over a one dimensional habitat, in which the free boundary represents the spreading front and is only caused by the prey. In these two problems, it is assumed that the species can only invade further into the new environment from the right end of the habitat, and the spreading front expands at a speed that is proportional to the prey’s population gradient at the front. Asymptotic behaviors of solution as are discussed firstly. The acquired results can help us to comprehend whether the expanding is successful or not. Then we establish the criteria for spreading and vanishing.
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