scholarly journals The nonlocal inverse problem of the identification of the lowest coefficient and the right-hand side in a second-order parabolic equation with integral conditions

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Elvin I. Azizbayov
Keyword(s):  
Inverse Problem ◽  
Parabolic Equation ◽  
Second Order ◽  
Integral Conditions ◽  
Order Parabolic Equation ◽  
Right Hand ◽  
The Right

scholarly journals Identification of spacewise dependent right-hand side in two dimensional parabolic equation

2021 ◽  
Vol 2092 (1) ◽  
pp. 012019
Author(s):  
LingDe Su ◽  
V. I. Vasil’ev
Keyword(s):  
Inverse Problem ◽  
Parabolic Equation ◽  
Numerical Solution ◽  
Hand Function ◽  
Adjoint Operator ◽  
Two Dimensional ◽  
Right Hand ◽  
Final Time Point ◽  
The Right ◽  
Constructed Self

Abstract In this paper numerical solution of the inverse problem of determining a spacewise dependent right-hand side function in two dimensional parabolic equation is considered. Usually, the right-hand side function dependent on spatial variable is obtained from measured data of the solution at the final time point. Many mathematical modeling problems in the field of physics and engineering will encounter the inverse problems to identify the right-hand terms. When studying an inverse problem of identifying the spacewise dependent right-hand function, iterative methods are often used. We propose a new conjugate gradient method based on the constructed self-adjoint operator of the equation for numerical solution of the function and numerical examples illustrate the efficiency and accuracy.

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