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Tumor growth with a necrotic core as an obstacle problem in pressure
Authors
Xu'an Dou
Chengfeng Shen
Zhennan Zhou
Publication date
31 August 2023
Publisher
View
on
arXiv
Abstract
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
)
\Omega(t)
Ω
(
t
)
, and the coincidence set
Λ
(
t
)
\Lambda(t)
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
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oai:arXiv.org:2309.00065
Last time updated on 12/09/2023