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Asymptotic behavior of solutions for competitive models with a free boundary

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  • In this paper, we study a competitive model involving two species separated by a free boundary by virtue of strong competition. When the initial data has positive lower bounds near $\pm\infty$, we prove that the solution converges, as $t\rightarrow \infty$, to a traveling wave solution and the free boundary moves to infinity with a constant speed.
    Mathematics Subject Classification: Primary: 35B40, 35K57; Secondary: 35R35.


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