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Simultaneous Identification of Two Time Independent Coefficients in a Nonlinear Phase Field System

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Abstract

In this article, we study a simultaneous reconstruction of two time independent parameters in a nonlinear phase field system by final overdetermination data. To this end, the given problem is transformed into an optimization problem by using the optimal control framework; then the existence of the minimizer for the control functional is established. Further, we deduce the necessary condition for the minimizer of the control functional. Finally we derive the stability estimate for two coefficients with the upper bound given by some Sobolev norms of the final measurement of the solutions.

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Acknowledgements

The authors are highly grateful to the referee(s) for their valuable comments and suggestions for improving the paper.

The first author is supported by Council of Scientific and Industrial Research (CSIR), India (Grant No. 09/472(0143)/2010-EMR-I).

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Author notes

  1. N. Barani Balan

    Present address: Department of Mathematics, Central University of Tamilnadu, Thiruvarur, 610004, India

Authors and Affiliations

  1. Department of Mathematics, Bharathiar University, Coimbatore, 641046, India

    S. Gnanavel, N. Barani Balan & K. Balachandran

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  1. S. Gnanavel
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  2. N. Barani Balan
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  3. K. Balachandran
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Correspondence to S. Gnanavel.

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Communicated by Firdaus E. Udwadia.

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Gnanavel, S., Barani Balan, N. & Balachandran, K. Simultaneous Identification of Two Time Independent Coefficients in a Nonlinear Phase Field System. J Optim Theory Appl 160, 992–1008 (2014). https://doi.org/10.1007/s10957-012-0251-y

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  • DOI: https://doi.org/10.1007/s10957-012-0251-y

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