scholarly journals Well-Posedness of the Right-Hand Side Identification Problem for a Parabolic Equation

2014 ◽  
Vol 66 (2) ◽  
pp. 165-177 ◽  
Author(s):  
A. Ashyralyev ◽  
A. S. Erdogan
Keyword(s):  
Parabolic Equation ◽  
Identification Problem ◽  
Well Posedness ◽  
Right Hand ◽  
The Right

scholarly journals A Note on the Right-Hand Side Identification Problem Arising in Biofluid Mechanics

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Abdullah Said Erdogan
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Identification Problem ◽  
Well Posedness ◽  
Space Operator ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Right Hand ◽  
Variable Space ◽  
The Right

The inverse problem of reconstructing the right-hand side (RHS) of a mixed problem for one-dimensional diffusion equation with variable space operator is considered. The well-posedness of this problem in Hölder spaces is established.

On the determination of the right-hand side in a parabolic equation

2012 ◽  
Vol 62 (11) ◽  
pp. 1672-1683 ◽  
Author(s):  
A. Ashyralyev ◽  
A.S. Erdogan ◽  
O. Demirdag
Keyword(s):  
Parabolic Equation ◽  
Right Hand ◽  
The Right

On the continuity of solutions of the equations of a porous medium and the fast diffusion with weighted and singular lower-order terms

2021 ◽  
Vol 18 (1) ◽  
pp. 104-139
Author(s):  
Yevhen Zozulia
Keyword(s):  
Porous Medium ◽  
Parabolic Equation ◽  
Harnack Inequality ◽  
Lower Order ◽  
Riesz Potential ◽  
Fast Diffusion ◽  
Right Hand ◽  
Continuity Of Solutions ◽  
The Right ◽  
Lower Order Terms

For the parabolic equation $$ \ v\left(x \right)u_{t} -{div({\omega(x)u^{m-1}}} \nabla u) = f(x,t)\: ,\; u\geq{0}\:,\; m\neq{1} $$ we prove the continuity and the Harnack inequality for generalized k solutions, by using the weighted Riesz potential on the right-hand side of the equation.

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.

scholarly journals Parabolic time dependent source identification problem with involution and Neumann condition

2021 ◽  
Vol 102 (2) ◽  
pp. 5-15
Author(s):  
A. Ashyralyev ◽  
◽  
A.S. Erdogan ◽  
◽  
◽  
...  
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Parabolic Equation ◽  
Source Identification ◽  
Parabolic Problem ◽  
Identification Problem ◽  
Time Dependent ◽  
Neumann Condition ◽  
Stability Estimates ◽  
Well Posedness

A time dependent source identification problem for parabolic equation with involution and Neumann condition is studied. The well-posedness theorem on the differential equation of the source identification parabolic problem is established. The stable difference scheme for the approximate solution of this problem and its stability estimates are presented. Numerical results are given.

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