2025/09/19 by Chen‐Chih Lai, Lai, Chen-Chih, Hongbo Lu +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth
paper · pdf · doi:10.48550/arxiv.2509.16416
openalex publication_date 2025/09/19 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28
We rigorously derive the joint limit of vanishing viscosity, singular pressure, and discrete-to-continuous phenotype structure in a class of tissue growth models. Starting from a viscoelastic (Brinkman-type) system describing multiple interacting phenotypes, where pressure depends nonlinearly on total cell density, we establish convergence to an incompressible Darcy-type model with a continuous phenotypic structure. Our analysis builds upon recent advances on the Brinkman-to-Darcy limit and incompressible transitions by David, Jacob, and Kim [arXiv:2503.18870], and on hydrodynamic limits for phenotype-structured populations by Debiec, Mandal, and Schmidtchen [J. Differential Equations 2025]. A key novelty lies in combining all three singular limits simultaneously, under uniform a priori estimates, compactness in space-phenotype-time, and a generalized entropy-dissipation structure. This provides a unified framework for modeling constrained tissue growth with mechanical feedback and phenotypic plasticity.