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Two-dimensional individual clustering model

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  • This paper is devoted to study a model of individual clustering with two specific reproduction rates in two space dimensions. Given $q>2$ and an initial condition in $W^{1,q}(\Omega)$, the local existence and uniqueness of solution have been shown in [6]. In this paper we give a detailed proof of existence of global solution.
    Mathematics Subject Classification: Primary: 35K20, 35B40, 35M33, 35J47, 35Q92.


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  • [1]

    H. Amann, "Linear and Quasilinear Parabolic Problems. Volume I . Abstract Linear Theory," Monographs in Mathematics, 89, Birkhäuser Boston, Inc., Boston, MA, 1995.doi: 10.1007/978-3-0348-9221-6.


    T. Cazenave and A. Haraux, "An Introduction to Semilinear Evolution Equations," Oxford Lecture Series in Mathematics and it Applications, 13, The Clarendon Press, Oxford University Press, New York, 1998.


    J. P. Dias, A simplified variational model for the bidimensional coupled evolution equations of a nematic liquid crystal, J. Math. Anal. Appl., 67 (1979), 525-541.doi: 10.1016/0022-247X(79)90041-6.


    J. P. Dias, Un problème aux limites pour un système d'équations non linéaires tridimensionnel, Bolletino U. M. I. B (5), 16 (1979), 22-31.


    P. Grindrod, Models of individual aggregation or clustering in single and multi-species communities, J. Math. Biol., 26 (1988), 651-660.doi: 10.1007/BF00276146.


    E. Nasreddine, Well-posedness for a model of individual clustering, arXiv:1211.2969v1, (2012).


    M. Schoenauer, Quelques résultats de régularité pour un système elliptique avec conditions aux limites couplées, Annales de la Faculté des Sciences de Toulouse 5e Série, 2 (1980), 125-135.doi: 10.5802/afst.550.


    Y. Tao and M. Winkler, Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity, J. Differential Equations, 252 (2012), 692-715.doi: 10.1016/j.jde.2011.08.019.

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