二维单向强退化抛物型方程的参数识别反问题  

Inverse problems of the parameter identification for two dimensional one-way strongly degenerate parabolic equations

作　　者：洪宇翔 王泽文 徐定华[2] HONG Yuxiang;WANG Zewen;XU Dinghua(School of Science,East China University of Technology,Nanchang 330013,China;School of Science,Zhejiang Sci-Tech University,Hangzhou 310018,China)

机构地区：[1]东华理工大学理学院,南昌330013 [2]浙江理工大学理学院,杭州310018

出　　处：《浙江理工大学学报（自然科学版）》2023年第3期388-395,共8页Journal of Zhejiang Sci-Tech University(Natural Sciences)

基　　金：国家自然科学基金项目(11961002,11861007);江西省自然科学基金重点项目(20212ACB201001);东华理工大学研究生创新项目(DHYC-201929)。

摘　　要：针对矩形区域内两种形式的强退化扩散系数,研究了二维单向强退化抛物型方程中扩散项的参数识别反问题。首先,利用Hölder不等式等证明了扩散项参数识别的唯一性和条件稳定性;然后,给出了数值计算强退化抛物型方程正问题的一种交替方向有限差分隐格式;最后,通过将退化扩散项的参数识别反问题归结为泛函优化问题,提出了基于遗传算法的退化项参数识别方法。计算模拟结果表明,退化项参数能被附加的测量数据有效识别出来,且提出的基于遗传算法的退化项参数识别方法具有很强的鲁棒性。The inverse problems of the parameter identification of diffusion terms in two-dimensional unidirectional strongly degenerate parabolic equation were studied for two forms of strongly degenerate diffusion coefficients in the rectangular domain.Firstly,the uniqueness and conditional stability of the parameter identification of the diffusion terms were proved by using such mathematical tools as Hölder inequality.Then,an alternating direction finite difference implicit scheme was proposed for the numerical calculation of the forward problem of strongly degenerate parabolic equations.Finally,a parameter identification method of degenerate terms based on genetic algorithm was proposed by reducing the inverse problems of the parameter identification of degenerate diffusion terms to a functional optimization problem.The simulation results show that the degenerate parameters can be effectively identified by the additional measurement data,and the proposed method based on genetic algorithm has strong robustness.

关 键 词：强退化 抛物型方程 参数识别 有限差分 遗传算法 

分 类 号：O175.26[理学—数学]