2023/08/31 by Xu’an Dou, Dou, Xu'an, Chengfeng Shen +3
Biochemistry, Genetics and Molecular Biology · Mathematics · #35C07 #35R35 #92C10 #Analysis of PDEs (math.AP) #Cellular Mechanics and Interactions #FOS: Mathematics #Mathematical Biology Tumor Growth #Microtubule and mitosis dynamics
paper · pdf · doi:10.48550/arxiv.2309.00065
openalex publication_date 2023/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motivated by the incompressible limit of a cell density model, we propose a free boundary tumor growth model where the pressure satisfies an obstacle problem on an evolving domain Ω(t), and the coincidence set Λ(t) captures the emerging necrotic core. We contribute to the analytical characterization of the solution structure in the following two aspects. By deriving a semi-analytical solution and studying its dynamical behavior, we obtain quantitative transitional properties of the solution separating phases in the development of necrotic cores and establish its long time limit with the traveling wave solutions. Also, we prove the existence of traveling wave solutions incorporating non-zero outer densities outside the tumor bulk, provided that the size of the outer density is below a threshold.