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Stability results for backward heat equations with time-dependent coefficient in the Banach space Lp(R )
Tác giả: Nguyen Van Duc , Phạm Quy Muoi, Nguyen Thị Van Anh
181    13
Applied Numerical Mathematics
Quyển: 175     Trang: 40-55
Đường link/DOI: https://www.sciencedirect.com/science/article/abs/pii/S0168927422000290
Minh chứng: 1534-2022-duc-muoi-vananh-anm.pdf
Năm xuất bản: 5/2022
Tóm tắt
In this paper, we investigate the problem of backward heat equations with time-dependent coefficient in the Banach space L_p(R), p>1. For this problem, we first prove the stability estimates of Hölder type. After that the Tikhonov-type regularization is applied to solve the problem. A priori and a posteriori parameter choice rules are investigated, which yield error estimates of Hölder type. Numerical implementations are presented to show the validity of the proposed scheme.
Từ khóa
Backward heat equationsTime-dependent coefficientsStability estimates of Hölder typeTikhonov-type regularizationA priori parameter choice ruleA posteriori parameter choice rule
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 coefficientsIdentifying an unknown source term of a parabolic equation in Banach spacesHình học FractalGiáo trình Độ đo và tích phânThe quasi-reversibility method for an inverse source problem for time-space fractional parabolic equationsA 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]