应用数学和力学2025，Vol.46Issue(10)：1354-1366,13.DOI:10.21656/1000-0887.450160
非线性相场模型的多参数反演问题
Multi-Parameter Inverse Problems of the Nonlinear Phase Field Model
摘要
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.关键词
反问题/非线性相场模型/最优控制/存在性/稳定性/唯一性Key words
inverse problem/nonlinear phase-field model/optimal control/existence/stability/uniqueness分类
数学引用本文复制引用
田瑜,杨柳,伊海鸿..非线性相场模型的多参数反演问题[J].应用数学和力学,2025,46(10):1354-1366,13.基金项目
国家自然科学基金(61663018 （）
11961042) （）
甘肃省自然科学基金(22JR5RA341) （22JR5RA341）
