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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.


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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) $

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