Bunting, Gary; Du, Yihong; Krakowski, Krzysztof Spreading speed revisited: analysis of a free boundary model. (English) Zbl 1302.35194 Netw. Heterog. Media 7, No. 4, 583-603 (2012). 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. Cited in 156 Documents 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 Keywords:diffusive logistic equation; free boundary; spreading-vanishing dichotomy; invasive population; spreading speed Citations:Zbl 1219.35373; Zbl 1275.35156; Zbl 1222.35096 PDFBibTeX XMLCite \textit{G. Bunting} et al., Netw. Heterog. Media 7, No. 4, 583--603 (2012; Zbl 1302.35194) Full Text: DOI