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.

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}, pages = {279--305}, publisher = {Elsevier}, volume = {32}, number = {2}, year = {2015}, doi = {10.1016/j.anihpc.2013.11.004}, mrnumber = {3325238}, zbl = {1321.35263}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2013.11.004/} }

TY - JOUR AU - Du, Yihong AU - Liang, Xing TI - Pulsating semi-waves in periodic media and spreading speed determined by a free boundary model JO - Annales de l'I.H.P. Analyse non linéaire PY - 2015 SP - 279 EP - 305 VL - 32 IS - 2 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2013.11.004/ DO - 10.1016/j.anihpc.2013.11.004 LA - en ID - AIHPC_2015__32_2_279_0 ER -

%0 Journal Article %A Du, Yihong %A Liang, Xing %T Pulsating semi-waves in periodic media and spreading speed determined by a free boundary model %J Annales de l'I.H.P. Analyse non linéaire %D 2015 %P 279-305 %V 32 %N 2 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2013.11.004/ %R 10.1016/j.anihpc.2013.11.004 %G en %F 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://archive.numdam.org/articles/10.1016/j.anihpc.2013.11.004/

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