# American Institute of Mathematical Sciences

March  2018, 13(1): 47-67. doi: 10.3934/nhm.2018003

## Stationary solutions and asymptotic behaviour for a chemotaxis hyperbolic model on a network

 Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica, Universitá degli Studi di L'Aquila, Via Vetoio, I-67100 Coppito (L'Aquila), Italy

Received  November 2016 Revised  October 2017 Published  March 2018

This paper approaches the question of existence and uniqueness of stationary solutions to a semilinear hyperbolic-parabolic system and the study of the asymptotic behaviour of global solutions. The system is a model for some biological phenomena evolving on a network composed by a finite number of nodes and oriented arcs. The transmission conditions for the unknowns, set at each inner node, are crucial features of the model.

Citation: Francesca R. Guarguaglini. Stationary solutions and asymptotic behaviour for a chemotaxis hyperbolic model on a network. Networks & Heterogeneous Media, 2018, 13 (1) : 47-67. doi: 10.3934/nhm.2018003
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Example of acyclic network; the highlighted arcs form the path linking the nodes $N_4$ and $N_5$.
Example: the highlighted arcs form the path from the outer point $e_1$ to the inner node $N_4$ and $I_5$ is an arc incident with $N_4$, not belonghing to the path.
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