Dissipative Gradient Nonlinearities Prevent δ$\delta$‐Formations in Local and Nonlocal Attraction–Repulsion Chemotaxis Models
ABSTRACT We study a class of zero‐flux attraction–repulsion chemotaxis models, characterized by nonlinearities laws for the diffusion of the cell density , the chemosensitivities and the production rates of the chemoattractant and the chemorepellent . In addition, a source involving also the gradient of is incorporated. Our overall study touches on different aspects: we address questions connected to local well‐posedness, we derive sufficient conditions to ensure boundedness of solutions, and finally, we develop numerical simulations giving insights into the evolution of the system.
Authors
- Alessandro Columbu
- Giuseppe Viglialoro (ORCID: https://orcid.org/0000-0002-2994-4123)
- Daniel Acosta‐Soba (ORCID: https://orcid.org/0000-0002-2159-5926)
- Tongxing Li (ORCID: https://orcid.org/0000-0003-2159-1949)
Institutions
- Shandong University (CN)
- University of Cagliari (IT)
- University of Tennessee at Chattanooga (US)
- Universidad de Cádiz (ES)
Publication Details
- Journal
- Studies in Applied Mathematics
- Published
- 2025-02-01
- DOI
- https://doi.org/10.1111/sapm.70018
- Citations
- 35
- Primary Topic
- Mathematical Biology Tumor Growth
- Type
- article
- Field-Weighted Citation Impact
- 47.88
Funders
- National Science Foundation
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- University of Central Arkansas
- Fondazione di Sardegna
- University of Tennessee at Chattanooga
- National Natural Science Foundation of China
- Ministero dell’Istruzione, dell’Università e della Ricerca
- Universidad de Cádiz
- Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni