### Abstract

This paper presents a semigroup approach for inverse source problems for the abstract heat equation, when the measured output data is given in subject to the integral overspecification over the spatial domain. The existence of a solution to the inverse source problem is shown in appropriate function spaces and a representation formula for the solution is proposed. Such representation permits the derivation of sufficient conditions for the uniqueness of the solution. Also an approximation method based on the optimal homotopy analysis method (OHAM) is designed, and the error estimates are discussed using graphical analysis. Moreover, we conjecture that our approach can be applied for the determination of a control parameter in an inverse problem with integral overspecialization data. The proposed algorithm is examined through various numerical examples for the reconstruction of continuous sources and the determination of a control parameter in parabolic equations. The accuracy and stability of the method are discussed and compared with several finite-difference techniques. Computational results show efficiency and high accuracy of the proposed algorithm.

Original language | English |
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Pages (from-to) | 397-409 |

Number of pages | 13 |

Journal | Journal of Computational and Applied Mathematics |

Volume | 313 |

DOIs | |

Publication status | Published - 15 Mar 2017 |

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### Keywords

- Homotopy analysis method
- Identification problem
- Inverse source problem
- Semigroup theory

### ASJC Scopus subject areas

- Computational Mathematics
- Applied Mathematics

### Cite this

**Identification of time-dependent source terms and control parameters in parabolic equations from overspecified boundary data.** / Jaradat, Ali; Awawdeh, Fadi; Md. Noorani, Mohd. Salmi.

Research output: Contribution to journal › Article

*Journal of Computational and Applied Mathematics*, vol. 313, pp. 397-409. https://doi.org/10.1016/j.cam.2016.09.029

}

TY - JOUR

T1 - Identification of time-dependent source terms and control parameters in parabolic equations from overspecified boundary data

AU - Jaradat, Ali

AU - Awawdeh, Fadi

AU - Md. Noorani, Mohd. Salmi

PY - 2017/3/15

Y1 - 2017/3/15

N2 - This paper presents a semigroup approach for inverse source problems for the abstract heat equation, when the measured output data is given in subject to the integral overspecification over the spatial domain. The existence of a solution to the inverse source problem is shown in appropriate function spaces and a representation formula for the solution is proposed. Such representation permits the derivation of sufficient conditions for the uniqueness of the solution. Also an approximation method based on the optimal homotopy analysis method (OHAM) is designed, and the error estimates are discussed using graphical analysis. Moreover, we conjecture that our approach can be applied for the determination of a control parameter in an inverse problem with integral overspecialization data. The proposed algorithm is examined through various numerical examples for the reconstruction of continuous sources and the determination of a control parameter in parabolic equations. The accuracy and stability of the method are discussed and compared with several finite-difference techniques. Computational results show efficiency and high accuracy of the proposed algorithm.

AB - This paper presents a semigroup approach for inverse source problems for the abstract heat equation, when the measured output data is given in subject to the integral overspecification over the spatial domain. The existence of a solution to the inverse source problem is shown in appropriate function spaces and a representation formula for the solution is proposed. Such representation permits the derivation of sufficient conditions for the uniqueness of the solution. Also an approximation method based on the optimal homotopy analysis method (OHAM) is designed, and the error estimates are discussed using graphical analysis. Moreover, we conjecture that our approach can be applied for the determination of a control parameter in an inverse problem with integral overspecialization data. The proposed algorithm is examined through various numerical examples for the reconstruction of continuous sources and the determination of a control parameter in parabolic equations. The accuracy and stability of the method are discussed and compared with several finite-difference techniques. Computational results show efficiency and high accuracy of the proposed algorithm.

KW - Homotopy analysis method

KW - Identification problem

KW - Inverse source problem

KW - Semigroup theory

UR - http://www.scopus.com/inward/record.url?scp=84993939948&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84993939948&partnerID=8YFLogxK

U2 - 10.1016/j.cam.2016.09.029

DO - 10.1016/j.cam.2016.09.029

M3 - Article

VL - 313

SP - 397

EP - 409

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

ER -