On a backward heat problem with time-dependent coefficient: Regularization and error estimates

2013 ◽  
Vol 219 (11) ◽  
pp. 6066-6073 ◽  
Author(s):  
Tuan Nguyen Huy ◽  
Quan Pham Hoang ◽  
Trong Dang Duc ◽  
Triet Le Minh
Keyword(s):  
Error Estimates ◽  
Time Dependent ◽  
Heat Problem ◽  
Backward Heat Problem

On an asymmetric backward heat problem with the space and time-dependent heat source on a disk

2019 ◽  
Vol 27 (1) ◽  
pp. 103-115
Author(s):  
Triet Minh Le ◽  
Quan Hoang Pham ◽  
Phong Hong Luu
Keyword(s):  
Exact Solution ◽  
Heat Source ◽  
Stable Solution ◽  
Time Dependent ◽  
Polar Coordinates ◽  
Heat Problem ◽  
Space And Time ◽  
Boundary Value Method ◽  
Ill Posed ◽  
Backward Heat Problem

Abstract In this article, we investigate the backward heat problem (BHP) which is a classical ill-posed problem. Although there are many papers relating to the BHP in many domains, considering this problem in polar coordinates is still scarce. Therefore, we wish to deal with this problem associated with a space and time-dependent heat source in polar coordinates. By modifying the quasi-boundary value method, we propose the stable solution for the problem. Furthermore, under some initial assumptions, we get the Hölder type of error estimates between the exact solution and the approximated solution. Eventually, a numerical experiment is provided to prove the effectiveness and feasibility of our method.

scholarly journals Two-Parameter Regularization Method for a Nonlinear Backward Heat Problem with a Conformable Derivative

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Vu Ho ◽  
Donal O’Regan ◽  
Hoa Ngo Van
Keyword(s):  
Integral Equation ◽  
Regularization Method ◽  
Time Variable ◽  
Conformable Derivative ◽  
Heat Problem ◽  
Regularization Parameters ◽  
Ill Posed ◽  
Parameter Regularization ◽  
Two Parameter ◽  
Backward Heat Problem

In this paper, we consider the nonlinear inverse-time heat problem with a conformable derivative concerning the time variable. This problem is severely ill posed. A new method on the modified integral equation based on two regularization parameters is proposed to regularize this problem. Numerical results are presented to illustrate the efficiency of the proposed method.

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