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    Asymptotics of steady states of a selection–mutation equation for small mutation rate

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    Type
    Article
    Authors
    Calsina, Àngel
    Cuadrado, Sílvia
    Desvillettes, Laurent
    Raoul, Gaël
    KAUST Grant Number
    KUK-I1-007-43
    Date
    2013-12-03
    Online Publication Date
    2013-12-03
    Print Publication Date
    2013-12
    Permanent link to this record
    http://hdl.handle.net/10754/597628
    
    Metadata
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    Abstract
    We consider a selection-mutation equation for the density of individuals with respect to a continuous phenotypic evolutionary trait. We assume that the competition term for an individual with a given trait depends on the traits of all the other individuals, therefore giving an infinite-dimensional nonlinearity. Mutations are modelled by means of an integral operator. We prove existence of steady states and show that, when the mutation rate goes to zero, the asymptotic profile of the population is a Cauchy distribution. © Royal Society of Edinburgh 2013.
    Citation
    Calsina À, Cuadrado S, Desvillettes L, Raoul G (2013) Asymptotics of steady states of a selection–mutation equation for small mutation rate. Proceedings of the Royal Society of Edinburgh: Section A Mathematics 143: 1123–1146. Available: http://dx.doi.org/10.1017/S0308210510001629.
    Sponsors
    A.C. and S. C. were partly supported by Grant nos MTM2008-06349-C03-03, 2009-SGR-345 and MTM2011-27739-C04-02. L. D. and G. R. were partly supported by Project CBDif-Fr ANR-08-BLAN-0333-01. G. R. was partly supported by Award no. KUK-I1-007-43 of Peter A. Markowich, made by the King Abdullah University of Science and Technology (KAUST). Finally, all authors were partly supported by the bilateral PICASSO project POLYCELL, Grant no. 22978WA.
    Publisher
    Cambridge University Press (CUP)
    Journal
    Proceedings of the Royal Society of Edinburgh: Section A Mathematics
    DOI
    10.1017/S0308210510001629
    ae974a485f413a2113503eed53cd6c53
    10.1017/S0308210510001629
    Scopus Count
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