Attractor of a nonlinear hybrid reaction–diffusion model of neuroendocrine transdifferentiation of human prostate cancer cells with time-lags

Kaihong Zhao; Kaihong Zhao

doi:10.3934/math.2023737

AIMS Mathematics

2023, Volume 8, Issue 6: 14426-14448. doi: 10.3934/math.2023737

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Research article

Attractor of a nonlinear hybrid reaction–diffusion model of neuroendocrine transdifferentiation of human prostate cancer cells with time-lags

Kaihong Zhao ^,

Department of Mathematics, School of Electronics & Information Engineering, Taizhou University, Taizhou 318000, Zhejiang, China

Received: 16 February 2023 Revised: 10 March 2023 Accepted: 14 March 2023 Published: 19 April 2023
MSC : 35K57, 35K61, 35B40, 92C60

Prostate cancer is a serious disease that endangers men's health. The genetic mechanism and treatment of prostate cancer have attracted the attention of scientists. In this paper, we focus on the nonlinear mixed reaction diffusion dynamics model of neuroendocrine transdifferentiation of prostate cancer cells with time delays, and reveal the evolutionary mechanism of cancer cells mathematically. By applying operator semigroup theory and the comparison principle of parabolic equation, we study the global existence, uniqueness and boundedness of the positive solution for the model. Additionally, the global invariant set and compact attractor of the positive solution are obtained by Kuratowski's measure of noncompactness. Finally, we use the Pdepe toolbox of MATLAB to carry out numerical calculations and simulations on an example to check the correctness and effectiveness of our main results. Our results show that the delay has no effect on the existence, uniqueness, boundedness and invariant set of the solution, but will affect the attractor.
- human prostate cancer cells,
- nonlinear hybrid reaction–diffusion model,
- time–lags,
- well-posedness,
- invariant set and compact attractor
Citation: Kaihong Zhao. Attractor of a nonlinear hybrid reaction–diffusion model of neuroendocrine transdifferentiation of human prostate cancer cells with time-lags[J]. AIMS Mathematics, 2023, 8(6): 14426-14448. doi: 10.3934/math.2023737

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Abstract

Prostate cancer is a serious disease that endangers men's health. The genetic mechanism and treatment of prostate cancer have attracted the attention of scientists. In this paper, we focus on the nonlinear mixed reaction diffusion dynamics model of neuroendocrine transdifferentiation of prostate cancer cells with time delays, and reveal the evolutionary mechanism of cancer cells mathematically. By applying operator semigroup theory and the comparison principle of parabolic equation, we study the global existence, uniqueness and boundedness of the positive solution for the model. Additionally, the global invariant set and compact attractor of the positive solution are obtained by Kuratowski's measure of noncompactness. Finally, we use the Pdepe toolbox of MATLAB to carry out numerical calculations and simulations on an example to check the correctness and effectiveness of our main results. Our results show that the delay has no effect on the existence, uniqueness, boundedness and invariant set of the solution, but will affect the attractor.

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