Symmetry analysis of an acid-mediated cancer invasion model

Juya Cui; Ben Gao; Juya Cui; Ben Gao

doi:10.3934/math.2022930

AIMS Mathematics

2022, Volume 7, Issue 9: 16949-16961. doi: 10.3934/math.2022930

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Research article

Symmetry analysis of an acid-mediated cancer invasion model

Juya Cui ^{1
,
,},
Ben Gao ²

1.
Department of Lymphoma, Shanxi Bethune Hospital, Shanxi Academy of Medical Sciences, Taiyuan, Shanxi 030032, China
2.
College of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi 030024, China

Received: 21 February 2022 Revised: 30 June 2022 Accepted: 11 July 2022 Published: 18 July 2022
MSC : 35E05, 35J05, 43A80

Under investigation in this paper is a reaction-diffusion system, which describes acid-mediated tumor growth. First, in view of Lie group analysis, infinitesimal generators of the considered system are presented. At the same time, some group invariant solutions are computed using reduced equations. In particular, we construct explicit solutions by applying the power-series method. Furthermore, the convergence of the solutions of the power-series is certificated. Finally, the stability behavior of the model can be understood by analyzing the solutions of different parameters.
- tumor growth,
- symmetries,
- power-series solutions
Citation: Juya Cui, Ben Gao. Symmetry analysis of an acid-mediated cancer invasion model[J]. AIMS Mathematics, 2022, 7(9): 16949-16961. doi: 10.3934/math.2022930

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Abstract

Under investigation in this paper is a reaction-diffusion system, which describes acid-mediated tumor growth. First, in view of Lie group analysis, infinitesimal generators of the considered system are presented. At the same time, some group invariant solutions are computed using reduced equations. In particular, we construct explicit solutions by applying the power-series method. Furthermore, the convergence of the solutions of the power-series is certificated. Finally, the stability behavior of the model can be understood by analyzing the solutions of different parameters.

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