非线性相场模型的多参数反演问题

田瑜; 杨柳; 伊海鸿

doi:10.21656/1000-0887.450160

非线性相场模型的多参数反演问题

doi: 10.21656/1000-0887.450160

兰州交通大学数理学院, 兰州 730070

基金项目:

国家自然科学基金(61663018；11961042)；甘肃省自然科学基金(22JR5RA341)

详细信息

作者简介:
田瑜（1998—）,女,硕士生(E-mail: tianyuyu815@163.com )；杨柳（1977—）,女,教授,博士(通讯作者. E-mail: l_yang218@163.com).

通讯作者:
杨柳（1977—）,女,教授,博士(通讯作者. E-mail: l_yang218@163.com).

中图分类号: O175.26
计量
- 文章访问数: 30
- HTML全文浏览量: 9
- PDF下载量: 1
- 被引次数: 0
出版历程
- 收稿日期: 2024-05-30
- 修回日期: 2024-06-27
- 网络出版日期: 2025-11-13

Multi-Parameter Inverse Problems of the Nonlinear Phase Field Model

School of Mathematics and Science, Lanzhou Jiaotong University, Lanzhou 730070, P.R.China

Funds:

The National Science Foundation of China(61663018；11961042)

摘要

摘要: 研究了在给定终端观测数据的附加条件下,同时反演非线性相场模型中两个与时间无关系数的反问题.与通常的抛物型方程不同,该文研究的是一个非线性抛物型方程组.首先,基于最优控制理论,将原问题转换成一个优化问题,通过构造相应的控制泛函,证明控制泛函极小元的存在性.其次,得到控制泛函极小元所满足的必要条件.最后,利用能量模估计的方法,成功地证明了控制泛函极小元的稳定性和唯一性.
- 反问题 /
- 非线性相场模型 /
- 最优控制 /
- 存在性 /
- 稳定性 /
- 唯一性
Abstract: The inverse problem of simultaneously inverting 2 time-independent coefficients in the nonlinear phase-field model was investigated with given terminal measurement data. Unlike the usual parabolic equations, a nonlinear parabolic system of equations was studied. Based on the optimal control framework, the inverse problem was transformed into an optimization problem. The existence and necessary condition of the minimizer for the cost functional were established. The uniqueness and stability of the minimizer were deduced from the necessary condition.
- inverse problem /
- nonlinear phase-field model /
- optimal control /
- existence /
- stability /
- uniqueness

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参考文献(17)

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