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Existence of nontrivial steady states for populations structured with respect to space and a continuous trait

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  • We prove the existence of nontrivial steady states to reaction-diffusion equations with a continuous parameter appearing in selection/mutation/competition/migration models for populations, which are structured both with respect to space and a continuous trait.
    Mathematics Subject Classification: Primary: 45K05, 92D15; Secondary: 92D25.

    Citation:

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  • [1]

    H. Brezis, "Analyse Fonctionnelle," Masson, Paris, 1987.

    [2]

    F. Brezzi and G. Gilardi, "Fundamentals of P.D.E. for Numerical Analysis," preprint n. 446 of Istituto di Analisi Numerica, Pavia, 1984.

    [3]

    A. Calsina and S. Cuadrado, Asymptotic stability of equilibria of selection-mutation equations, J. Math. Biol., 54 (2007), 489-511.doi: doi:10.1007/s00285-006-0056-4.

    [4]

    J. Carrillo, L. Desvillettes and K. Fellner, Exponential decay towards equilibrium for the inhomogeneous Aizenman-Bak model, Commun. Math. Phys., 278 (2008), 433-451.doi: doi:10.1007/s00220-007-0404-2.

    [5]

    J. Carrillo, L. Desvillettes and K. Fellner, Fast-reaction limit for the inhomogeneous Aizenman-Bak model, Kinetic and Related Models, 1 (2008), 127-137.

    [6]

    R. Dautray and J.-L. Lions, "Mathematical Analysis and Numerical Methods for Science and Technology," vol 1. Physical Origins and Classical Methods, Springer-Verlag, Berlin-Heidelberg-New York, 1990.

    [7]

    L. Desvillettes, R. Ferrières and C. Prévost, "Infinite Dimensional Reaction-Diffusion for Population Dynamics," preprint n. 2003-04 du CMLA, ENS de Cachan.

    [8]

    L. Desvillettes, P.-E. Jabin, S. Mischler and G. Raoul, On mutation-selection dynamics, Commun. Math. Sc., 6 (2008), 729-747.

    [9]

    O. Diekmann, P.-E. Jabin, S. Mischler and B. Perthame, The dynamics of adaptation: An illuminating example and a Hamilton-Jacobi approach, Theor. Popul. Biol., 67 (2005), 257-271.doi: doi:10.1016/j.tpb.2004.12.003.

    [10]

    P. Laurençot and S. Mischler, Global existence for the discrete diffusive coagulation-fragmentation equations in L1, Rev. Mat. Iberoamericana, 18 (2002), 731-745.

    [11]

    P. Laurençot and S. Mischler, The continuous coagulation-fragmentation equations with diffusion, Arch. Rational Mech. Anal., 162 (2002), 45-99.

    [12]

    G. Raoul, Local stability of evolutionary attractors for continuous structured populations, to appear in Monatshefte für Mathematik, 2011.

    [13]

    F. Rothe, "Global Solutions of Reaction-Diffusion Systems," Lecture Notes in Mathematics, vol. 1072. Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 1984.

    [14]

    J. Smoller, "Shock Waves and Reaction-Diffusion Equations," Second edition, Grundlehren der Mathematischen Wissenschaften, vol. 258. Springer-Verlag, New York, 1994.

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