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In this paper, we mainly discuss the Lotka-Volterra competition model with Robin boundary and free boundary conditions, and discuss the long time asymptotic behaviour of solutions in the weak-strong competition case. When g∞<∞ the inferior competitor p can not spread successfully as t→∞. While for the superior competitor q, there are two cases: One is when g∞≤ R*, q will die out eventually; the other is when g∞>R*, q can spread successfully. However, when g∞=∞, both p and q have upper and lower bounds.

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