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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.
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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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, Tome 32 (2015) no. 2, pp. 279-305. doi: 10.1016/j.anihpc.2013.11.004
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