2025/07/15 by David Gómez‐Castro, Gómez-Castro, David
Mathematics · Medicine · #35Q70 #35Q92 #45K05 #65M08 #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2507.11132
openalex publication_date 2025/07/15 · openalex created_date 2025/10/08 · openalex updated_date 2026/07/28
In [Bailo, Carrillo, Hu. SIAM J. Appl. Math. 2023] the authors introduce a finite-volume method for aggregation-diffusion equations with non-linear mobility. In this paper we prove convergence of this method using an Aubin--Simons compactness theorem due to Gallouët and Latché. We use suitable discrete H1 and W-1,1 discrete norms. We provide two convergence results. A first result shows convergence with general entropies (U) (including singular and degenerate) if the initial datum does not have free boundaries, the mobility is Lipschitz, and the confinement (V) and aggregation (K) potentials are W2,∞0. A second result shows convergence when the initial datum has free boundaries, mobility is just continuous, and V and K are W1,∞, but under the assumption that the entropy U is C1 and strictly convex.