Publication de 12 numéros par an
ISSN Imprimer: 1064-2315
ISSN En ligne: 2163-9337
Indexed in
The Minimax Problems of Pointwise Observation for a Parabolic Boundary-Value Problem
RÉSUMÉ
We consider the problems of minimax estimation of linear functionals from solutions of boundary-value problem for parabolic equations at pointwise observations. At first, the case of separate error restrictions is considered. Such problem is equivalent to the optimal pulse control problem. We obtain the results of minimax estimation in the problem when measurements are taken from some ellipsoid (a-minimax estimations). We suggest an approach for finding the approximating a0-minimax estimations which save a feature of the theorem about representation. One is to solve the problem of optimal control and the problem of one-dimensional optimization to find these estimations.
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Mashchenko S. O., Kapustian D. O., The Problem of a Function Maximization on a Type-2 Fuzzy Set, in Modern Mathematics and Mechanics, 2019. Crossref
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Nakonechnyi O. G., Kapustian O. A., Chikrii A. O., Approximate Guaranteed Mean Square Estimates of Functionals on Solutions of Parabolic Problems with Fast Oscillating Coefficients Under Nonlinear Observations, Cybernetics and Systems Analysis, 55, 5, 2019. Crossref
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Zgurovsky Michael Z., D’Apice Ciro, De Maio Umberto, Gorban Nataliia V., Kasyanov Pavlo O., Kapustyan Oleksiy V., Khomenko Olha V., Valero José, Uniform Global Attractor for a Class of Nonautonomous Evolution Hemivariational Inequalities with Multidimensional “Reaction-Velocity” Law, in Contemporary Approaches and Methods in Fundamental Mathematics and Mechanics, 2021. Crossref
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Kapustian O. A., Nakonechnyi O. G., Approximate Minimax Estimation of Functionals of Solutions to the Wave Equation under Nonlinear Observations, Cybernetics and Systems Analysis, 56, 5, 2020. Crossref