On a Relaxed Cahn–Hilliard Tumor Growth Model with Single-Well Potential and Degenerate Mobility
Abstract. We consider a phase-field system modeling solid tumor growth. This system consists of a Cahn–Hilliard equation coupled with a nutrient equation. The former is characterized by a degenerate mobility and a singular potential. Both equations are subject to suitable reaction terms which model proliferation and nutrient consumption. Chemotactic effects are also taken into account. Adding an elliptic regularization, depending on a relaxation parameter [Formula: see text], in the equation for the chemical potential, we prove the existence of a weak solution to an initial and boundary value problem for the relaxed system. Then, we let [Formula: see text] go to zero, and we recover the existence of a weak solution to the original system.
Authors
- Matteo Fornoni (ORCID: https://orcid.org/0000-0002-9787-047X)
- Maurizio Grasselli (ORCID: https://orcid.org/0000-0003-2521-2926)
- Benoît Perthame B (ORCID: https://orcid.org/0000-0002-7091-1200)
- Cecilia Cavaterra (ORCID: https://orcid.org/0000-0002-2754-7714)
Institutions
- Centre National de la Recherche Scientifique (FR)
- University of Milan (IT)
- Université Paris Cité (FR)
- Sorbonne Université (FR)
- Istituto di Matematica Applicata e Tecnologie Informatiche (IT)
- Laboratoire Jacques-Louis Lions (FR)
- MUSCLEES: Compréhension mathématique multi-échelles d'écosystèmes vivants complexes avec structures émergentes (FR)
- Politecnico di Milano (IT)
Publication Details
- Journal
- SIAM Journal on Mathematical Analysis
- Published
- 2026-11-02
- DOI
- https://doi.org/10.1137/25m183273x
- Primary Topic
- Mathematical Biology Tumor Growth
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- Università degli Studi di Milano
- Politecnico di Milano
- Sorbonne Université
- Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni