Abstract
Recent work establishes that the solution of the parameter estimation on a perforated domain can be approximated by instead solving the inverse problem on the much easier to work with associated solid domain. In this work, we consider vector-valued variational problems on a perforated domain and show that the inverse problems on the perforated and associated solid domains can be similarly connected. The approach relies on a “generalized collage theorem” built from the vector-valued Lax-Milgram Theorem in reflexive Banach spaces. The method will be demonstrated on a numerical example.
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References
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Acknowledgements
This research was partially supported by Natural Sciences and Engineering Research Council of Canada (NSERC) in the form of a Discovery Grant (HK) and by project MTM2016-80676-P (AEI/FEDER, UE).
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Kunze, H., La Torre, D., Ruiz Galán, M. (2018). Using the Collage Method to Solve Inverse Problems for Vector-Valued Variational Problems on a Perforated Domain in Reflexive Banach Spaces. In: Kilgour, D., Kunze, H., Makarov, R., Melnik, R., Wang, X. (eds) Recent Advances in Mathematical and Statistical Methods . AMMCS 2017. Springer Proceedings in Mathematics & Statistics, vol 259. Springer, Cham. https://doi.org/10.1007/978-3-319-99719-3_10
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DOI: https://doi.org/10.1007/978-3-319-99719-3_10
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