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Stability results for weak solutions to backward one-dimensional semi-linear parabolic equations with locally Lipschitz source
Tác giả: Đinh Nho Hào, Nguyễn Văn Đức, Nguyễn Thị Ngọc Oanh
278    0
Journal of Inverse and Ill-posed Problems
Quyển: 29/4     Trang: 499-513
Đường link/DOI: https://www.degruyter.com/document/doi/10.1515/jiip-2020-0125/html?lang=de
Năm xuất bản: 7/2021
Tóm tắt
Stability estimates of Hölder type for weak solutions to backward one-dimensional semi-linear parabolic equations with locally Lipschitz source are obtained. It is noticed that stability results for weak solutions to nonlinear inverse problems are very rare in the literature.
Từ khóa
Backward semi-linear parabolic equations, locally Lipschitz source, ill-posed problems, stability estimate, weak solution
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 equationsIdentifying 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 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]Regularization of backward parabolic equations in Banach spaces by generalized Sobolev equations