Asymptotic behavior of a nonlinear necrotic tumor model with a periodic external nutrient supply

Junde Wu; Shihe Xu

doi:10.3934/dcdsb.2020018

Article Contents

2020, Volume 25, Issue 7: 2453-2460. Doi: 10.3934/dcdsb.2020018

This issue Previous Article Dynamical analysis of a diffusive SIRS model with general incidence rate Next Article Random dynamics of lattice wave equations driven by infinite-dimensional nonlinear noise

Asymptotic behavior of a nonlinear necrotic tumor model with a periodic external nutrient supply

Junde Wu^1, , and
Shihe Xu^2,

1.
Department of Mathematics, Soochow University, Suzhou, Jiangsu 215006, China
2.
School of Mathematics and Statistics, Zhaoqing University, Zhaoqing, Guangdong 526061, China

^* Corresponding author: Junde Wu
^* Corresponding author: Junde Wu

Received: May 31, 2019

Revised: July 31, 2019

Early access: April 2020

Published: July 2020

The second author is supported by the National Natural Science Foundation of China under grant 11301474 and the Natural Science Foundation of Guangdong Province under grant 2018A030313536

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Abstract

In this paper we study a nonlinear free boundary problem for the growth of radially symmetric tumor with a necrotic core. The proliferation of tumor cells depends on the concentration of nutrient which satisfies a diffusion equation within tumor and is periodically supplied by external tissues. The tumor outer surface and the inner interface of the necrotic core are both free boundaries. We give a sufficient and necessary condition for the existence and uniqueness of positive periodic solution, and show it is globally asymptotically stable under radial perturbations. Our analysis implies that tumor growth may finally synchronize the periodic external nutrient supply.

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Mathematics Subject Classification: Primary: 35B10, 35B35, 35R35; Secondary: 35Q92.

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References

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