Fokker-Planck方程的一个精确解
An Exact Solution of the Fokker-Planck Equation
摘要: 本文首先利用一个变换将描述肿瘤增长模型的Fokker-Planck方程转化为常微分方程,然后利用F-展开法和Mathematica软件构造出方程的一个精确解,最后描绘在不同参数情形下解的图像来展示解的性态。
Abstract: We first use a transform to convert the Fokker-Planck equation describing the tumor growth model into an ordinary differential equation, then construct an exact solution of the equation by means of the F-expansion method and Mathematica software, and finally draw the figures of the solutions under the different choosing parameters to demonstrate the behaviors of the solutions.
文章引用:卓玛代吉, 索南旺毛, 扎西拉姆, 义西卓玛. Fokker-Planck方程的一个精确解[J]. 应用数学进展, 2021, 10(1): 211-217. https://doi.org/10.12677/AAM.2021.101024

参考文献

[1] 史现花. CRE方法在非线性偏微分方程中的应用[D]: [硕士学位论文]. 西安: 西北大学, 2017.
[2] 张鹏鸽, 高淑萍, 朱佑彬. 肿瘤细胞增长模型的分析与研究[J]. 生物数学学报, 2016, 31(2): 239-242.
[3] Rotenberg, M. (1982) Theory of Distributed Quiescent State in the Cell Cycle. Journal of Theoretical Biology, 96. 495-509. [Google Scholar] [CrossRef] [PubMed]
[4] Rotenberg, M. (1983) Transport Theory for Growing Cell Populations. Journal of Theoretical Biology, 103, 181-199. [Google Scholar] [CrossRef] [PubMed]
[5] Zhang, Z.Y. and Li, G.F. (2020) Communications in Nonlinear Science and Numerical Simulation, 93, Article Number: 105506.
[6] Zhang, W.G., Chang, Q.S. and Jiang, B.G. (2002) Explicit Exact Solitary-Wave Solutions for Compound KdV-Type and Compound KdV-Burgers-Type Equations with Nonlinear Terms of Any Order. Chaos, Solitons and Fractals, 13, 311-319. [Google Scholar] [CrossRef
[7] 范恩贵, 张鸿庆. 非线性孤子方程的齐次平衡法[J]. 物理学报, 1998(3): 4-13.
[8] 王小艳. Jacobi椭圆函数展开解及在非线性偏微分方程中的应用[D]: [硕士学位论文]. 沈阳: 东北大学, 2014.
[9] 王书敏, 薛瑞梅, 姚若侠. 非线性偏微分方程的精确行波解[J]. 计算机技术与发展, 2019, 29(2): 101-105.
[10] 詹艺珩. (G'/G)展开法及F展开法在非线性发展方程求解中的应用[D]: [硕士学位论文]. 南充: 西华师范大学, 2019.