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On some model problem for the propagation of interacting species in a special environment

  • * Corresponding author: Mingmin Zhang

    * Corresponding author: Mingmin Zhang
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  • The purpose of this note is to study the existence of a nontrivial solution for an elliptic system which comes from a newly introduced mathematical problem so called Field-Road model. Specifically, it consists of coupled equations set in domains of different dimensions together with some interaction of non classical type. We consider a truncated problem by imposing Dirichlet boundary conditions and an unbounded setting as well.

    Mathematics Subject Classification: 35J47, 35J57.

    Citation:

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  • Figure 1.  The domain $ \Omega_\ell $ for one-road problem

    Figure 2.  The domain $ \Omega_\ell $ for two-road problem

    Figure 3.  The graph of the function $ \rho(x_1) $

  • [1] H. Amann, Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Review, 18 (1976), 620-709.  doi: 10.1137/1018114.
    [2] H. BerestyckiJ.-M. Roquejoffre and L. Rossi, The influence of a line with fast diffusion on Fisher-KPP propagation, J. Math. Biol., 66 (2013), 743-766.  doi: 10.1007/s00285-012-0604-z.
    [3] H. BerestyckiJ.-M. Roquejoffre and L. Rossi, Fisher-KPP propagation in the presence of a line: Further effects, Nonlinearity, 26 (2013), 2623-2640.  doi: 10.1088/0951-7715/26/9/2623.
    [4] H. BerestyckiJ.-M. Roquejoffre and L. Rossi, Travelling waves, spreading and extinction for Fisher-KPP propagation driven by a line with fast diffusion, Nonlinear Analysis, 137 (2016), 171-189.  doi: 10.1016/j.na.2016.01.023.
    [5] P. G. Ciarlet, Linear and Nonlinear Functional Analysis with Applications, SIAM, Philadelphia, 2013.
    [6] M. Chipot, Elliptic Equations: An Introductory Course, Birkh$\ddot{ a }$user, Basel, Birkh$\ddot{ a }$user Advanced Texts, 2009. doi: 10.1007/978-3-7643-9982-5.
    [7] M. ChipotAsymptotic Issues for Some Partial Differential Equations, Imperial College Press, London, 2016.  doi: 10.1142/p1064.
    [8] R. Dautray and J.-L. Lions, Analyse Mathématique et Calcul Numérique pour les Sciences et les Techniques, Tome 1, Masson, Paris, 1985.
    [9] L. C. Evans, Partial Differential Equations, Volume 19 of Graduate Studies in Mathematics, American Mathematical Society, 2$^{nd}$ edition, 2010. doi: 10.1090/gsm/019.
    [10] D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 2001.
    [11] L. Rossi, A. Tellini and E. Valdinoci, The effect on Fisher-KPP propagation in a cylinder with fast diffusion on the boundary, SIAM J. Math. Anal., 49 (2017), 4595–4624. doi: 10.1137/17M1125388.
    [12] A. Tellini, Propagation speed in a strip bounded by a line with different diffusion, J. Differential Equations, 260 (2016), 5956-5986.  doi: 10.1016/j.jde.2015.12.028.
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