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.

scholarly journals A note on the parabolic identification problem with involution and Dirichlet condition

2020 ◽  
Vol 99 (3) ◽  
pp. 130-139
Author(s):  
A. Ashyralyev ◽  
◽  
A.S. Erdogan ◽  
A. Sarsenbi ◽  
◽  
...  
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Difference Scheme ◽  
Source Identification ◽  
Parabolic Problem ◽  
Identification Problem ◽  
Dirichlet Condition ◽  
Stability Estimates ◽  
Well Posedness ◽  
The Difference

A space source of identification problem for parabolic equation with involution and Dirichlet 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 is presented. Furthermore, stability estimates for the difference scheme of the source identification parabolic problem are presented. Numerical results are given.

scholarly journals A note on well-posedness of source identification elliptic problem in a Banach space

2020 ◽  
Vol 99 (3) ◽  
pp. 96-104
Author(s):  
A. Ashyralyev ◽  
◽  
C. Ashyralyyev ◽  
V.G. Zvyagin ◽  
◽  
...  
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Elliptic Problem ◽  
Source Identification ◽  
Elliptic Equations ◽  
Identification Problem ◽  
Stability Estimates ◽  
Well Posedness ◽  
Identification Problems ◽  
Coercive Stability

We study the source identification problem for an elliptic differential equation in a Banach space. The exact estimates for the solution of source identification problem in H¨older norms are obtained. In applications, four elliptic source identification problems are investigated. Stability and coercive stability estimates for solution of source identification problems for elliptic equations are obtained.

scholarly journals Well-posedness of boundary value problems for reverse parabolic equation with integral condition

2018 ◽  
Vol 1 (1) ◽  
pp. 11-21
Author(s):  
Charyyar Ashyralyyev
Keyword(s):  
Parabolic Equation ◽  
Boundary Value Problems ◽  
Parabolic Problem ◽  
Boundary Value ◽  
Integral Condition ◽  
Stability Estimates ◽  
Well Posedness ◽  
Holder Space ◽  
Hölder Space ◽  
Coercive Stability

AbstractReverse parabolic equation with integral condition is considered. Well-posedness of reverse parabolic problem in the Hölder space is proved. Coercive stability estimates for solution of three boundary value problems (BVPs) to reverse parabolic equation with integral condition are established.

Numerical solution of a source identification problem: Almost coercivity

2019 ◽  
Vol 27 (4) ◽  
pp. 457-468 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Abdullah Said Erdogan ◽  
Ali Ugur Sazaklioglu
Keyword(s):  
Numerical Solution ◽  
Source Identification ◽  
Identification Problem ◽  
Second Order ◽  
Numerical Results ◽  
Difference Schemes ◽  
Stability Estimates ◽  
Order Of Accuracy ◽  
Accuracy Difference ◽  
Coercive Stability

Abstract The present paper is devoted to the investigation of a source identification problem that describes the flow in capillaries in the case when an unknown pressure acts on the system. First and second order of accuracy difference schemes are presented for the numerical solution of this problem. Almost coercive stability estimates for these difference schemes are established. Additionally, some numerical results are provided by testing the proposed methods on an example.

scholarly journals On a nonlocal problem for parabolic equation with time dependent coefficients

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nguyen Duc Phuong ◽  
Ho Duy Binh ◽  
Le Dinh Long ◽  
Dang Van Yen
Keyword(s):  
Parabolic Equation ◽  
Mild Solution ◽  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Nonlocal Problem ◽  
Point Theory ◽  
Time Dependent ◽  
Well Posedness ◽  
Conformable Derivative

AbstractThis paper is devoted to the study of existence and uniqueness of a mild solution for a parabolic equation with conformable derivative. The nonlocal problem for parabolic equations appears in many various applications, such as physics, biology. The first part of this paper is to consider the well-posedness and regularity of the mild solution. The second one is to investigate the existence by using Banach fixed point theory.

scholarly journals A note on the hyperbolic-parabolic identification problem with involution and Dirichlet boundary condition

2020 ◽  
Vol 99 (3) ◽  
pp. 120-129
Author(s):  
Maksat Ashyraliyev ◽  
◽  
Maral A. Ashyralyyeva ◽  
Allaberen Ashyralyev ◽  
◽  
...  
Keyword(s):  
Source Identification ◽  
Test Problem ◽  
Dirichlet Boundary ◽  
Identification Problem ◽  
Dirichlet Condition ◽  
Stability Estimates ◽  
Simple Test ◽  
Order Of Accuracy ◽  
First Order ◽  
The Stability

In the present paper, a source identification problem for hyperbolic-parabolic equation with involution and Dirichlet condition is studied. The stability estimates for the solution of the source identification hyperbolicparabolic problem are established. The first order of accuracy stable difference scheme is constructed for the approximate solution of the problem under consideration. Numerical results are given for a simple test problem.

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