在数学生物学中出现的几个合PDE系统的反向问题上
Ming-Hui Ding1, Hongyu Liu2, Guang-Hui Zheng3
1Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong, China.
Journal of mathematical biology
|November 13, 2023
概括
本研究涉及与非负解相结合的部分微分方程 (PDEs) 的反向问题. 我们开发了一种新的方法,使用平均边界流量数据独特识别未知系数,克服了重大挑战.
科学领域:
- 应用数学 应用数学 应用数学
- 科学计算科学计算
- 数学生物学 数学生物学
背景情况:
- 反向问题对于从观测数据中确定系统参数至关重要.
- 结合的部分微分方程 (PDEs) 模型复杂的系统在生物学和生态学.
- 非负的解决方案对于现实的生物和生态解释是必不可少的.
研究的目的:
- 为了研究与非负解相结合的PDE系统的反向问题.
- 通过使用平均边界流量数据来确定未知的系数.
- 为应对数据减少,非线性合和非负性约束所带来的挑战.
主要方法:
- 开发一种新的方案来解决合 PDE 的反向问题.
- 使用受控注入源项来生成多个平均流量数据集.
- 利用合PDE系统结构固有的单调性特性.
主要成果:
- 在合的PDE系统中实现未知系数的唯一识别.
- 证明拟议方法的有效性,尽管数据减少和非线性合.
- 建立一个强大的方法来解决具有挑战性的反向问题与非消极性约束.
结论:
- 拟议的方法成功地识别了合PDE系统中的未知系数.
- 该方法适用于现实世界的生物和生态建模场景.
- 这项工作促进了应用科学中复杂的反向问题的理解和解决.
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