文章基本信息

标题：Identification of source term for the ill-posed Rayleigh–Stokes problem by Tikhonov regularization method
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作者：Tran Thanh Binh ; Hemant Kumar Nashine ; Le Dinh Long 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2019
卷号：2019
期号：1
页码：1-20
DOI：10.1186/s13662-019-2261-7
出版社：Hindawi Publishing Corporation
摘要：In this paper, we study an inverse source problem for the Rayleigh–Stokes problem for a generalized second-grade fluid with a fractional derivative model. The problem is severely ill-posed in the sense of Hadamard. To regularize the unstable solution, we apply the Tikhonov method regularization solution and obtain an a priori error estimate between the exact solution and regularized solutions. We also propose methods for both a priori and a posteriori parameter choice rules. In addition, we verify the proposed regularized methods by numerical experiments to estimate the errors between the regularized and exact solutions.
关键词：35K05;35K99;47J06;47H10;Rayleigh;Stokes problem;Fractional derivative;Ill-posed problem;Tikhonov regularization method