Identification of source term for the ill-posed Rayleigh–Stokes problem by Tikhonov regularization method
Trần Thanh BìnhFaculty of Natural Sciences, Thu Dau Mot University, Thu Dau Mot, VietnamHemant Kumar NashineDepartment of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, IndiaLe Dinh LongInstitute of Computational Science and Technology, Ho Chi Minh City, VietnamNguyen Hoang LucInstitute of Research and Development, Duy Tan University, Da Nang 550000, VietnamNguyen Huu CanApplied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
2019en
ABI
Аннотация
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.
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