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Asymptotic behavior of solutions of Fisher-KPP equation with free boundary conditions. (English) Zbl 1296.35217

Summary: We study a free boundary problem for the Fisher-KPP equation modeling the spreading of a biological or chemical species. In this model, the free boundaries represent the spreading fronts of the species. We discuss the asymptotic behavior of bounded solutions and obtain a trichotomous result: spreading (the free boundaries amount to the whole space and the solution converges to 1), transition (the free boundaries stay in a bounded interval and the solution converges to a stationary solution with positive compact support) and vanishing (the free boundaries converge to the same point and the solution tends to 0 within a finite time).

MSC:

35R35 Free boundary problems for PDEs
35B40 Asymptotic behavior of solutions to PDEs
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