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    Please use this identifier to cite or link to this item: http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/76897

    Title: Propagation and blocking in periodically hostile environments
    Authors: Guo, Jong-shenq;Hamel, Francois
    Contributors: 淡江大學數學學系
    Date: 2012-06
    Issue Date: 2012-05-22 17:06:33 (UTC+8)
    Publisher: Heidelberg: Springer
    Abstract: We study the persistence and propagation (or blocking) phenomena for a species in periodically hostile environments. The problem is described by a reaction-diffusion equation with zero Dirichlet boundary condition. We first derive the existence of a minimal nonnegative nontrivial stationary solution and study the large-time behavior of the solution of the initial boundary value problem. To the main goal, we then study a sequence of approximated problems in the whole space with reaction terms which are with very negative growth rates outside the domain under investigation. Finally, for a given unit vector, by using the information of the minimal speeds of approximated problems, we provide a simple geometric condition for the blocking of propagation and we derive the asymptotic behavior of the approximated pulsating travelling fronts. Moreover, for the case of constant diffusion matrix, we provide two conditions for which the limit of approximated minimal speeds is positive.
    Relation: Archive for Rational Mechanics and Analysis 204(3), pp.945-975
    DOI: 10.1007/s00205-012-0494-7
    Appears in Collections:[數學學系暨研究所] 期刊論文

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