Global smooth solutions for a hyperbolic chemotaxis model on a network

2014/11/22 by F.R. Guarguaglini, Roberto Natalini, Guarguaglini, Francesca Romana +1 · 2 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #35L50 #35M33 #35Q92 #35R02 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Gene Regulatory Network Analysis #Mathematical Biology Tumor Growth

paper · pdf · doi:10.48550/arxiv.1411.6109

openalex publication_date 2014/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study a semilinear hyperbolic-parabolic system modeling biological phenomena evolving on a network composed by oriented arcs. We prove the existence of global (in time) smooth solutions to this problem. The result is obtained by using energy estimates with suitable transmission conditions at nodes.

Citations

• Global Existence of Smooth Solutions for Partially Dissipative Hyperbolic Systems with a Convex Entropy

Cited by

• Selection of the ground state on a compact metric graph
• A relaxation scheme for the equations of isentropic gas dynamics on a network with jump transmission conditions

Related

• Stationary solutions and asymptotic behaviour for a chemotaxis hyperbolic model on a network
• Global solutions for a chemotaxis hyperbolic-parabolic system on networks with nonhomogeneous boundary conditions
• A hyperbolic model of chemotaxis on a network: a numerical study
• Parabolic models for chemotaxis on weighted networks
• Global solutions for a hyperbolic-parabolic system of chemotaxis