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Note on a two-species competition-diffusion model with two free boundaries. (English) Zbl 1371.35367

Summary: In [J.-S. Guo and C.-H. Wu, Nonlinearity 28, No. 1, 1–27 (2015; Zbl 1316.92066); C.-H. Wu, J. Differ. Equations 259, No. 3, 873–897 (2015; Zbl 1319.35081)], the authors studied a two-species competition-diffusion model with two free boundaries. These two free boundaries describing the spreading fronts of two competing species, respectively, may intersect each other as time evolves. The existence, uniqueness and long time behavior of global solution have been established. In this note we discuss the conditions for spreading and vanishing, and more accurate limits of \((u, v)\) as \(t \rightarrow \infty\) when spreading occurs. Some new results and simpler proofs will be provided.

MSC:

35R35 Free boundary problems for PDEs
35K51 Initial-boundary value problems for second-order parabolic systems
92B05 General biology and biomathematics
35B40 Asymptotic behavior of solutions to PDEs
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References:

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