一个具有Robin自由边界的双曲肿瘤生长模型解的定性分析

doi:10.12052/gdutxb.200109

Journal of Guangdong University of Technology ›› 2021, Vol. 38 ›› Issue (02): 60-65.doi: 10.12052/gdutxb.200109

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A Qualitative Analysis of a Hyperbolic Tumor Growth Model with Robin Free Boundary

Zhou Yun, Wei Xue-mei

School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China

Received:2020-08-28 Online:2021-03-10 Published:2021-01-13

Abstract

Abstract: A hyperbolic tumor growth model with Robin free boundary is studied, which contains an elliptic partial differential equation describing the concentration of nutrients, an ordinary differential equation describing the radius of tumor and two hyperbolic equations describing the growth of tumor cells. In this paper, by applying the method of characteristic curves and the Banach fixed point theorem, the existence and uniqueness of the global solution of the model are proven. Finally, it is proven that while ${K_R} = 0$, $\mathop {\lim }\limits_{t \to \infty } R\left( t \right) = \infty$.

Key words: tumor growth, free boundary problem, global solution

CLC Number:

O175

Zhou Yun, Wei Xue-mei. A Qualitative Analysis of a Hyperbolic Tumor Growth Model with Robin Free Boundary[J].Journal of Guangdong University of Technology, 2021, 38(02): 60-65.

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