Electron. J. Differential Equations, Vol. 2017 (2017), No. 200, pp. 1-15.

Optimization method for identifying the source term in an inverse wave equation

Arumugam Deiveegan, Periasamy Prakash, Juan Jose Nieto

Abstract:
In this work, we investigate the inverse problem of identifying a space-wise dependent source term of wave equation from the measurement on the boundary. On the basis of the optimal control framework, the inverse problem is transformed into an optimization problem. The existence and necessary condition of the minimizer for the cost functional are obtained. The projected gradient method and two-parameter model function method are applied to the minimization problem and numerical results are illustrated.

Submitted September 1, 2015. Published August 30, 2017.
Math Subject Classifications: 35L05, 35R30, 49J20.
Key Words: Inverse problem; source term; optimal control; model function.

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Arumugam Deiveegan
Department of Mathematics
Periyar University
Salem 636 011, India
email: deiveegan.a@gmail.com
Periasamy Prakash
Department of Mathematics
Periyar University
Salem 636 011, India
email: pprakashmaths@gmail.com
Juan Jose Nieto
Departamento de Análisis Matemático
Facultad de Matemáticas
Universidad de Santiago de Compostela
Santiago de Compostela 15782, Spain
email: juanjose.nieto.roig@usc.es

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