On a Nonlinear Hyperbolic–Elliptic System Modeling Chemotaxis

Flavia Smarrazzo ()
Additional contact information
Flavia Smarrazzo: Facoltà Dipartimentale di Ingegneria, Università Campus Bio-Medico di Roma, Via A. del Portillo 21, 00128 Roma, Italy

Mathematics, 2025, vol. 13, issue 21, 1-39

Abstract: In this paper, we study a hyperbolic–elliptic system with L 1 -initial data, which arises as a mathematical model for chemotaxis. In particular, after introducing the notion of entropy solutions in this setting, we prove results concerning the existence of solutions—either global or local in time—depending on how small the L 1 -norm of the initial data is. Furthermore, we prove the uniqueness of the entropy solutions by adapting the standard doubling-variable method for hyperbolic conservation laws to the current framework.

Keywords: hyperbolic–elliptic systems; entropy solutions; chemotaxis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/21/3523/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/21/3523/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:21:p:3523-:d:1786570

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().