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0212U002024,
0107U002539
,
Development of the methods and algorithms for analysis and optimal control of nonlinear singular systems.
Makarenko Oleksandr Sergeevich,
12-01-2012
Institute for Applied System Analysis at NASc and Ministry of Education of Ukraine
Functional-topological properties of the resolving operator for a class of multivariational inequalities in infitnite-dimensional spaces describing mathematical models of nonlinear stationary geophysical processes and fields different which contain differential equations with partial derivatives with explosive and multiple-valued dependence between determined parameters of a target problem are investigated. The problem of optimum control of essentially nonlinear degenerate elliptic is considered by a variational inequality where as the control act coefficients of main nonlinear elliptic operator. Necessary conditions of an optimality are received and proved by the example of a problem of optimum solenoidal control in coefficients for nonlinear elliptic the equations with regional Dirikhle conditions on border of area. The method of finite differences for evolutionary inclusions with +-коэрцитивными lambda-zero pseudomonotonic maps is proved also. The qualitative behaviour of solutions of infitnite-dimensional evolutional systems is investigated, in particular existence is proved and are found out topological characteristics of global attractor. For considered three-dimensional Benar system the existence of strongly continuous solutions is proved. Long-term forecasts of functions of a condition piesoelectric processes and fields with application of the theory global and trajectory attractors for m-semiflows are investigated. Relations between pull-back attractors problems of optimal control and global attractors of the three-dimensional Navje-Stoks system under condition of assumptions that globally certain strong solutions exist at any initial conditions in V are investigated.
Іваненко В.І.
Андрєєв М.В.
Горбань Н.В.
Дудников П.Й.
Задоянчук Н.В.
Капустян О.В.
Касьянов П.О.
Когут О.П.
Морева О.О.
Патіоха А.А.
Повещенко Г.П.
2020-04-02
Updated: 2025-12-07
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