scholarly journals An a posteriori parameter choice rule for the truncation regularization method for solving backward parabolic problems

2014 ◽  
Vol 255 ◽  
pp. 150-160 ◽  
Author(s):  
Yuan-Xiang Zhang ◽  
Chu-Li Fu ◽  
Yun-Jie Ma
Keyword(s):  
Regularization Method ◽  
Choice Rule ◽  
Parabolic Problems ◽  
A Posteriori ◽  
Parameter Choice ◽  
A Posteriori Parameter Choice

An a posteriori mollification method for the heat equation backward in time

2017 ◽  
Vol 25 (4) ◽  
Author(s):  
Nguyen Van Duc
Keyword(s):  
Heat Equation ◽  
Error Estimate ◽  
Regularization Method ◽  
Choice Rule ◽  
Stability Estimates ◽  
A Posteriori ◽  
Parameter Choice ◽  
A Posteriori Parameter Choice ◽  
Mollification Method ◽  
Derivatives Of

AbstractThe heat equation backward in timesubject to the constraintwhereAn a posteriori parameter choice rule for this regularization method is suggested, which yields the error estimateFurthermore, we establish stability estimates of Hölder type for all derivatives of the solutions with respect to

An a posteriori truncation regularization method for an ill-posed problem for the heat equation with an integral boundary condition

2019 ◽  
Vol 26 (1) ◽  
pp. 35-45
Author(s):  
Mohamed Denche ◽  
Abdelali Benchikha
Keyword(s):  
Boundary Condition ◽  
Heat Equation ◽  
Regularization Method ◽  
Initial Conditions ◽  
Integral Boundary Condition ◽  
A Posteriori ◽  
Parameter Choice ◽  
Integral Boundary ◽  
A Posteriori Parameter Choice ◽  
Ill Posed

Abstract The aim of this paper is to investigate the problem of control by the initial conditions of the heat equation with an integral boundary condition. Using the truncation method with an a posteriori parameter choice rule, we give the error estimate between the exact and the regularized solutions. A numerical implementation shows the efficiency of the proposed method.

scholarly journals A Posteriori Regularization Parameter Choice Rule for Truncation Method for Identifying the Unknown Source of the Poisson Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Xiao-Xiao Li ◽  
Dun-Gang Li
Keyword(s):  
Poisson Equation ◽  
Regularization Method ◽  
Regularization Parameter ◽  
Choice Rule ◽  
Conditional Stability ◽  
A Posteriori ◽  
Parameter Choice ◽  
Convergence Estimate ◽  
The Poisson Equation ◽  
Unknown Source

We consider the problem of determining an unknown source which depends only on one variable in two-dimensional Poisson equation. We prove a conditional stability for this problem. Moreover, we propose a truncation regularization method combined with an a posteriori regularization parameter choice rule to deal with this problem and give the corresponding convergence estimate. Numerical results are presented to illustrate the accuracy and efficiency of this method.

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