On Source Identification Problem for Telegraph Differential Equations

Ashyralyev, Allaberen; Çekiç, Fatma

doi:10.1007/978-3-319-32857-7_4

Cited by 12 publications

(8 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Source identification problems (SIPs) for partial differential equations (PDEs) are used to model physical and biological system engineering and sociological processes and have been studied by many authors (see [1–12] and the references given therein).…”

Section: Introduction and Formulation Of Problemmentioning

confidence: 99%

“…Theorems of coercive stability estimates (SEs) for the solution of BVPs for multidimensional elliptic equations were proved. SIP for a telegraph equation with unknown parameter in a Hilbert space with the self‐adjoint positive definite operator (SAPDO) was investigated [3]. Furthermore, theorems of SEs for the solution of the telegraph equation were proved.…”

Section: Introduction and Formulation Of Problemmentioning

confidence: 99%

See 1 more Smart Citation

On the absolute stable difference scheme for the space‐wise dependent source identification problem for elliptic‐telegraph equation

Ashyralyev

Al-Hammouri²,

Ashyralyyev

2020

Numerical Methods Partial

Self Cite

View full text Add to dashboard Cite

The present paper is devoted to study the first order of accuracy absolute stable difference scheme for the approximate solution of the space identification problem for the elliptic‐telegraph equation in Hilbert spaces with the self‐adjoint positive definite operator. The main theorem on the stability of the difference scheme is established. In applications, theorems on the stability of difference schemes for two types of the space identification problems for multidimensional elliptic‐telegraph partial differential equations are proved. Numerical analysis is provided.

show abstract

Section: Introduction and Formulation Of Problemmentioning

confidence: 99%

Section: Introduction and Formulation Of Problemmentioning

confidence: 99%

On the absolute stable difference scheme for the space‐wise dependent source identification problem for elliptic‐telegraph equation

Ashyralyev

Al-Hammouri²,

Ashyralyyev

2020

Numerical Methods Partial

Self Cite

View full text Add to dashboard Cite

show abstract

“…Source identification problems for partial differential equations are used to model biological, physical, system engineering, and sociological processes and have been studied by many authors (see other studies [1][2][3][4][5][6][7][8][9][10][11][12] and the references given therein).…”

Section: Introductionmentioning

confidence: 99%

“…Theorems of coercive stability estimates for the solution of boundary value problems for multidimensional elliptic equations were proved. Ashyralyev and Cekic 3 investigated the source identification problem for a telegraph equation with unknown parameter in a Hilbert space with the self‐adjoint positive definite operator. Theorems of stability estimates for the solution of the telegraph equation were proved.…”

Section: Introductionmentioning

confidence: 99%

Stability of the space identification problem for the elliptic‐telegraph differential equation

Ashyralyev

Al-Hammouri²

2020

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

The present paper is devoted to study the space identification problem for the elliptic-telegraph differential equation in Hilbert spaces with the self-adjoint positive definite operator. The main theorem on the stability of the space identification problem for the elliptic-telegraph differential equation is proved. In applications, theorems on the stability of three source identification problems for one dimensional with nonlocal conditions and multidimensional elliptic-telegraph differential equations are established.

show abstract

“…Telegraph equation is mostly interested in physical systems. Many physicists and engineers use telegraph equation without time delay (see, [13]- [17]), and also telegraph equation is studied by using classical energy methods and operator theory(see, [18]). For example, Ashyralyev and Modanli (see, [19]- [21]) studied the stability of Cauchy problem for telegraph differential and difference equations in a Hilbert space.…”

Section: Introductionmentioning

confidence: 99%