淡江大學機構典藏:Item 987654321/109369
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    Please use this identifier to cite or link to this item: https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/109369


    Title: LACK OF SYMMETRY IN LINEAR DETERMINACY DUE TO CONVECTIVE EFFECTS IN REACTION-DIFFUSION-CONVECTION PROBLEMS
    Authors: Ameera, Al-Kiffai;Crooks, Elaine
    Keywords: Travelling wave;linear determinacy;convection;reaction-diffusion;spreading speed
    Date: 2016-03
    Issue Date: 2017-01-17 10:18:22 (UTC+8)
    Publisher: 淡江大學出版中心
    Abstract: This paper is concerned with linear determinacy in monostable reaction- diffusion-convection equations and co-operative systems. We present sufficient conditions for minimal travelling-wave speeds (equivalent to spreading speeds) to equal values obtained from linearisations of the travelling-wave problem about the unstable equilibrium. These conditions involve both reaction and convection terms. We present separate conditions for non-increasing and non-decreasing travelling waves, called `right' and `left' conditions respectively, because of the asymmetry in propagation caused by the convection terms. We also give a necessary condition on the reaction term for the existence of convection terms such that both the right and left conditions can be satisfied simultaneously. Examples show that our sufficient conditions for linear determinacy are not necessary and compare these conditions in the scalar case with alternative conditions observed in Malaguti-Marcelli [15] and Benguria-Depassier-Mendez [3]. We also illustrate, for both an equation and a system, the existence of reaction and (non-trivial) convection terms for which the right and left linear determinacy conditions are simultaneously satisfied. An example is given of an equation which is right but not left linearly determinate.
    Relation: Tamkang Journal of Mathematics 47(1), pp.51-70
    DOI: 10.5556/j.tkjm.47.2016.1891
    Appears in Collections:[Tamkang Journal of Mathematics] v.47 n.1

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