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On Convergence of Difference Approximations of Extremum Problems Described by Elliptic Equations with Unbounded Nonlinearity

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Finite Difference Methods. Theory and Applications (FDM 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11386))

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Abstract

The present work is devoted to investigation of an optimization problem for elliptic equations with mixed derivatives and unbounded nonlinearity. The coefficients multiplying partial derivatives of the second order in the state equation are used as a control function. We develop finite difference approximations of extremum problems, study their well-posedness and estimate the approximation accuracy with respect to the state.

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Acknowledgments

The author thanks Prof. F. V. Lubyshev for his important remarks and useful discussions.

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Authors and Affiliations

  1. Bashkir State University, Zaki Validi Street, 32, Ufa, Republic of Bashkortostan, Russia

    Aigul Manapova

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  1. Aigul Manapova
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Correspondence to Aigul Manapova .

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Editors and Affiliations

  1. IICT, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Dimov

  2. Eötvös Loránd University, Budapest, Hungary

    István Faragó

  3. University of Rousse, Rousse, Bulgaria

    Lubin Vulkov

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Manapova, A. (2019). On Convergence of Difference Approximations of Extremum Problems Described by Elliptic Equations with Unbounded Nonlinearity. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Finite Difference Methods. Theory and Applications. FDM 2018. Lecture Notes in Computer Science(), vol 11386. Springer, Cham. https://doi.org/10.1007/978-3-030-11539-5_39

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  • DOI: https://doi.org/10.1007/978-3-030-11539-5_39

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-11538-8

  • Online ISBN: 978-3-030-11539-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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