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The quasi-reversibility method for an inverse source problem for time-space fractional parabolic equations
Tác giả: Nguyen Van Duc, Nguyen Van Thang, Nguyen Trung Thanh
83    5
Journal of Differential Equations
Quyển: 344     Trang: 102-130
Đường link/DOI: https://www.sciencedirect.com/science/article/abs/pii/S0022039622006106
Minh chứng: 1534_2023_Duc_Thang_Thanh_JDE.pdf
Năm xuất bản: 1/2023
Tóm tắt
`In this paper, we apply the quasi-reversibility method to solve an inverse source problem for a time-space fractional parabolic equation. Hölder-type error estimates for the regularized solutions are proved for both a priori and a posteriori regularization parameter choice rules. The theoretical error estimates are confirmed with numerical tests for one and two dimensional equations.
Từ khóa
Inverse source problems for time-space fractional parabolic equations, quasireversibility method, error estimates, numerical implementation
Cùng tác giả
A non-local boundary value problem method for semi-linear parabolic equations backward in time.Đánh giá ổn định cho các phương trình kiểu Burgers ngược thời gianA mollification method for semi-linear heat equations backward in time in the Banach space Lp(R)Giáo trình Giải tích (Tập 1)Stability Results for Semi-linear Parabolic Equations Backward in TimeAn a posteriori mollifcation method for the heat equation backward in timeBackward semi-linear parabolic equations with time-dependent coefficients and local Lipschitz sourceGiáo trình Giải tích 2Một phương pháp chỉnh hóa cho phương trình parabolic với hệ số phụ thuộc thời gianCác kết quả ổn định cho phương trình parabolic bậc phân ngược thời gianA Mollification Method for Backward Time-Fractional Heat EquationIdentifying an unknown source term in a time-space fractional parabolic equationRegularization of backward time-fractional parabolic equations by Sobolev-type equationsStability results for weak solutions to backward one-dimensional semi-linear parabolic equations with locally Lipschitz sourceIdentifying an unknown source term in a heat equation with time-dependent coefficientsStability results for backward heat equations with time-dependent coefficient in the Banach space Lp(R )Identifying an unknown source term of a parabolic equation in Banach spacesHình học FractalGiáo trình Độ đo và tích phânA coefficient identification problem for a system of advection-reaction equations in water quality modelingA regularization method for Caputo fractional derivatives in the Banach space L∞[0, T]