Global solutions for a chemotaxis hyperbolic-parabolic system on networks with nonhomogeneous boundary conditions

TL;DR

This paper investigates a chemotaxis model on networks, establishing conditions for stationary solutions and demonstrating their role as asymptotic profiles for global solutions.

Contribution

It introduces a framework for analyzing a hyperbolic-parabolic chemotaxis system on networks with nonhomogeneous boundary conditions, including existence and asymptotic behavior of solutions.

Findings

Existence of stationary solutions under certain boundary conditions

Stationary solutions serve as asymptotic profiles for global solutions

Conditions for flux-preserving transmission at network nodes

Abstract

In this paper we study a semilinear hyperbolic-parabolic system as a model for some chemotaxis phenomena evolving on networks; we consider transmission conditions at the inner nodes which preserve the fluxes and non- homogeneous boundary conditions having in mind phenomena with inflow of cells and food providing at the network exits. We give some conditions on the boundary data which ensure the existence of stationary solutions and we prove that these ones are asymptotic profiles for a class of global solutions.