Analysis of a nonlinear necrotic tumor model with angiogenesis and a periodic supply of external nutrients

Huijuan Song; Qian Huang; Zejia Wang

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arXiv · 2110.04688

Analysis of a nonlinear necrotic tumor model with angiogenesis and a periodic supply of external nutrients

Huijuan Song·Qian Huang·Zejia Wang

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Abstract

In this paper, we consider a free boundary problem modeling the growth of spherically symmetric necrotic tumors with angiogenesis and a $\omega$-periodic supply $\phi(t)$ of external nutrients. In the model, the consumption rate of the nutrient and the proliferation rate of tumor cells $S(\sigma)$ are both general nonlinear functions. The well-posedness and asymptotic behavior of solutions are studied. We show that if the average of $S(\phi(t))$ is nonpositive, then all evolutionary tumors will finally vanish; the converse is also ture. If instead the average of $S(\phi(t))$ is positive, then there exists a unique positive periodic solution and all other evolutionary tumors will converge to this periodic state.

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Huijuan Song, Qian Huang, Zejia Wang. 2021-10-10. Analysis of a nonlinear necrotic tumor model with angiogenesis and a periodic supply of external nutrients. https://arxiv.org/abs/2110.04688

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