Pulsating semi-waves in periodic media and spreading speed determined by a free boundary model
Annales de l'I.H.P. Analyse non linéaire, Volume 32 (2015) no. 2, p. 279-305
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We consider a radially symmetric free boundary problem with logistic nonlinear term. The spatial environment is assumed to be asymptotically periodic at infinity in the radial direction. For such a free boundary problem, it is known from [7] that a spreading-vanishing dichotomy holds. However, when spreading occurs, only upper and lower bounds are obtained in [7] for the asymptotic spreading speed. In this paper, we investigate one-dimensional pulsating semi-waves in spatially periodic media. We prove existence, uniqueness of such pulsating semi-waves, and show that the asymptotic spreading speed of the free boundary problem coincides with the speed of the corresponding pulsating semi-wave.

DOI : https://doi.org/10.1016/j.anihpc.2013.11.004
Classification:  35K20,  35R35,  35J60,  92B05
Keywords: Diffusive logistic equation, Free boundary, Periodic environment, Pulsating semi-wave, Spreading speed
@article{AIHPC_2015__32_2_279_0,
     author = {Du, Yihong and Liang, Xing},
     title = {Pulsating semi-waves in periodic media and spreading speed determined by a free boundary model},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {32},
     number = {2},
     year = {2015},
     pages = {279-305},
     doi = {10.1016/j.anihpc.2013.11.004},
     zbl = {1321.35263},
     mrnumber = {3325238},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2015__32_2_279_0}
}
Du, Yihong; Liang, Xing. Pulsating semi-waves in periodic media and spreading speed determined by a free boundary model. Annales de l'I.H.P. Analyse non linéaire, Volume 32 (2015) no. 2, pp. 279-305. doi : 10.1016/j.anihpc.2013.11.004. http://www.numdam.org/item/AIHPC_2015__32_2_279_0/

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