Abstract
In this article, we consider the optimal control problem governed by the wave equation in a 2-dimensional domain \(\Omega _{\epsilon }\) in which the state equation and the cost functional involves highly oscillating periodic coefficients \(A^\epsilon \) and \(B^\epsilon \), respectively. This paper aims to examine the limiting behavior of optimal control and state and identify the limit optimal control problem, which involves the influences of the oscillating coefficients.
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Acknowledgements
The first author is member of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM) and has been partially supported by GNAMPA (INDAM) under the project GNAMPA 2024 (CUP E53C23001670001), Italy. The second author acknowledges the Council of Scientific & Industrial Research (CSIR), for the Research Fellowship (09/1005(0035)/2020-EMR-I). The third author acknowledges the support from Science & Engineering Research Board (SERB) (EEQ/2023/000531), Government of India.
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Faella, L., Raj, R. & Sardar, B.C. Optimal control problem governed by wave equation in an oscillating domain and homogenization. Z. Angew. Math. Phys. 75, 52 (2024). https://doi.org/10.1007/s00033-024-02203-0
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DOI: https://doi.org/10.1007/s00033-024-02203-0