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 Quasi-boundary value method for non-well posed problem for a parabolic equation with integral boundary condition

2001 ◽  
Vol 7 (2) ◽  
pp. 129-145 ◽  
Author(s):  
M. Denche ◽  
K. Bessila
Keyword(s):  
Boundary Condition ◽  
Convergence Rates ◽  
Initial Conditions ◽  
Nonlocal Problem ◽  
Convergence Result ◽  
Integral Boundary Condition ◽  
Integral Boundary ◽  
Boundary Value Method ◽  
Ill Posed ◽  
Well Posed

In this paper we study the problem of control by the initial conditions of the heat equation with an integral boundary condition. This problem is ill-posed. Perturbing the final condition we obtain an approximate nonlocal problem depending on a small parameter. We show that the approximate problems are well posed. We also obtain estimates of the solutions of the approximate problems and a convergence result of these solutions. Finally, we give explicit convergence rates.

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

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