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

Francesca R. Guarguaglini; Francesca R. Guarguaglini

doi:10.3934/nhm.2018003

Networks and Heterogeneous Media

2018, Volume 13, Issue 1: 47-67. doi: 10.3934/nhm.2018003

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

Francesca R. Guarguaglini

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

Received: 01 November 2016 Revised: 01 October 2017
Primary: 35R02; Secondary: 35M33, 35L50, 35B40, 35Q92

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.
- Nonlinear hyperbolic systems,
- transmission conditions,
- stationary solutions,
- asymptotic behaviour of global solutions,
- chemotaxis
Citation: Francesca R. Guarguaglini. 2018: Stationary solutions and asymptotic behaviour for a chemotaxis hyperbolic model on a network, Networks and Heterogeneous Media, 13(1): 47-67. doi: 10.3934/nhm.2018003

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Abstract

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.

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