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