Global smooth solutions for a hyperbolic chemotaxis model on a network
Francesca Romana Guarguaglini, Roberto Natalini
TL;DR
This paper proves the existence of global smooth solutions for a hyperbolic chemotaxis model on a network, using energy estimates and transmission conditions at network nodes.
Contribution
It introduces a novel approach to establish global solutions for a hyperbolic chemotaxis system on networks, combining energy estimates with transmission conditions.
Findings
Existence of global smooth solutions established
Energy estimates used for proof
Transmission conditions at network nodes are crucial
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.
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Taxonomy
TopicsMathematical Biology Tumor Growth · Advanced Mathematical Modeling in Engineering · Gene Regulatory Network Analysis