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Stability results for backward heat equations with time-dependent coefficient in the Banach space Lp(R )
Authors: Nguyen Van Duc , Phạm Quy Muoi, Nguyen Thị Van Anh
303    64
Applied Numerical Mathematics
: 175     : 40-55
: https://www.sciencedirect.com/science/article/abs/pii/S0168927422000290
: 1534-2022-duc-muoi-vananh-anm.pdf
Publishing year: 5/2022
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.
Backward heat equationsTime-dependent coefficientsStability estimates of Hölder typeTikhonov-type regularizationA priori parameter choice ruleA posteriori parameter choice rule
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 coefficientsIdentifying an unknown source term of a parabolic equation in Banach spacesFractal 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]Regularization of backward parabolic equations in Banach spaces by generalized Sobolev equations