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

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• 作者：Ali Jaradat^a ; Fadi Awawdeh^b ; ^c ; ^{awawdeh@hu.edu.jo" class="auth_mail" title="E-mail the corresponding author} ; ^{fawawadeh@du.edu.om" class="auth_mail" title="E-mail the corresponding author} ; Mohd Salmi Md Noorani^a
• 关键词：Inverse source problem ; Identification problem ; Semigroup theory ; Homotopy analysis method
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：313
• 期：Complete
• 页码：397-409
• 全文大小：847 K

文摘

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.