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Spreading speed revisited: analysis of a free boundary model. (English) Zbl 1302.35194

Summary: We investigate, from a more ecological point of view, a free boundary model considered in [Y.-H. Du and Z.-G. Lin, SIAM J. Math. Anal. 42, No. 1, 377–405 (2010; Zbl 1219.35373); erratum ibid. 45, No. 3, 1995–1996 (2013; Zbl 1275.35156); Y.-H. Du and Z.-M. Guo, J. Differ. Equations 250, No. 12, 4336–4366 (2011; Zbl 1222.35096)] that describes the spreading of a new or invasive species, with the free boundary representing the spreading front. We derive the free boundary condition by considering a “population loss” at the spreading front, and correct some mistakes regarding the range of spreading speed in [Zbl 1219.35373]. Then we use numerical simulation to gain further insights to the model, which may help to determine its usefulness in concrete ecological situations.

MSC:

35K20 Initial-boundary value problems for second-order parabolic equations
35R35 Free boundary problems for PDEs
35K91 Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacian
92D25 Population dynamics (general)
92D40 Ecology
35J60 Nonlinear elliptic equations
92B05 General biology and biomathematics
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