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Identifying an unknown source term of a parabolic equation in Banach spaces
Authors: Nguyen Van Duc, Nguyen Van Thang, Luong Duy Nhat Minh, Nguyen Trung Thanh
209    15
Applicable Analysis
: 101(6)     : 2066-2084
: https://www.tandfonline.com/doi/abs/10.1080/00036811.2020.1800650
: 1534-2022-duc-thang-minh-thanh-aa.pdf
Publishing year: 4/2022
A new regularization method for an inverse source problem for a parabolic equation in a Banach space is proposed. Hölder-type error estimates for the regularized solutions are proved for both a priori and a posteriori regularization parameter choice rules. Some numerical examples are presented for illustrating the efficiency of the method.
Inverse source problems in Banach spaces; regularization; error estimates
A non-local boundary value problem method for semi-linear parabolic equations backward in time.Stability estimates for Burgers-type equations backward in timeA mollification method for semi-linear heat equations backward in time in the Banach space Lp(R)Analysis IStability 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 sourceA REGULARIZATION METHOD FOR BACKWARD PARABOLIC EQUATIONS WITH TIME-DEPENDENT COEFFICIENTSStability results for backward time-fractional parabolic equationsA 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 )Fractal GeometryTextbook of Measures and IntegralThe 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]