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

S. Gnanavel (), N. Barani Balan () and K. Balachandran ()
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S. Gnanavel: Bharathiar University
N. Barani Balan: Bharathiar University
K. Balachandran: Bharathiar University

Journal of Optimization Theory and Applications, 2014, vol. 160, issue 3, No 15, 992-1008

Abstract: 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.

Keywords: Inverse problem; Optimal control; Phase field system; Stability (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10957-012-0251-y

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