Differentiation of the functional in a parametric optimization problem for a coefficient of a semilinear elliptic equation
- Authors: Chernov A.V.1,2
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Affiliations:
- Lobachevskii State University of Nizhny Novgorod
- Nizhny Novgorod State Technical University
- Issue: Vol 53, No 4 (2017)
- Pages: 551-562
- Section: Control Theory
- URL: https://journal-vniispk.ru/0012-2661/article/view/154368
- DOI: https://doi.org/10.1134/S0012266117040139
- ID: 154368
Cite item
Abstract
We study parametric optimization with respect to an integral criterion of the higher coefficient and the right-hand side of a second-order semilinear elliptic equation with the Dirichlet boundary condition. We obtain formulas for the first partial derivatives of the objective functional with respect to the control parameters. The total preservation (preservation for the entire set of control parameters) of the unique solvability of the boundary value problem for this equation is proved based on the theory of monotone operators.
About the authors
A. V. Chernov
Lobachevskii State University of Nizhny Novgorod; Nizhny Novgorod State Technical University
Author for correspondence.
Email: chavnn@mail.ru
Russian Federation, Nizhny Novgorod, 603950; Nizhny Novgorod, 603600
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