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Jaradat, Ali; Awawdeh, Fadi; Noorani, Mohd Salmi Md

Identification of time-dependent source terms and control parameters in parabolic equations from overspecified boundary data. (English) Zbl 1353.65100

J. Comput. Appl. Math. 313, 397-409 (2017).
Summary: 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.

Cited in 2 Documents

MSC:

65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
35R30 Inverse problems for PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs

Keywords:

inverse source problem; identification problem; semigroup theory; homotopy analysis method; abstract heat equation; error estimate; algorithm; numerical example; stability

Software:

BVPh
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References:

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