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Toward Understanding the Boundary Propagation Speeds in Tumor Growth Models

At the continuous level, we consider two types of tumor growth models: the cell density model, based on the fluid mechanical construction, is more favorable for scientific interpretation and numerical simulations, and the free boundary model, as the incompressible limit of the former, is more tractable when investigating the boundary propagation. In this work, we aim to investigate the boundary propagation speeds in those models based on asymptotic analysis of the free boundary model and efficient numerical simulations of the cell density model. We derive, for the first time, some analytical solutions for the free boundary model with pressure jumps across the tumor boundary in multidimensions with finite tumor sizes. We further show that in the large radius limit, the analytical solutions to the free boundary model in one and multiple spatial dimensions converge to traveling wave solutions. The convergence rate in the propagation speeds are algebraic in multidimensions as opposed to the exponential convergence in one dimension. We also propose an accurate front capturing numerical scheme for the cell density model, and extensive numerical tests are provided to illustrate the analytical findings.

Ketersediaan

Informasi Detail

Judul Seri

SIAM JOURNAL ON APPLIED MATHEMATICS; Vol.81 No.3 May-June 2021

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 1052 - 1076

Bahasa

English

ISBN/ISSN

-

Klasifikasi

-

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

TUMOR GROWTH MODELS
BRINKMAN MODEL
FREE BOUNDARY MODEL
FRONT CAPTURING SCHEME

Info Detail Spesifik

https://doi.org/10.1137/19M1296665

Pernyataan Tanggungjawab

Jian-Guo Liu, Min Tang, Li Wang, Zhennan Zhou

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