Differential-operator inclusions and evolutionary variational inequalities in infinite-dimensional spaces

Research manager O.S. Makarenko.

 

The results of the research significantly promote the development of nonlinear differential equations theory with multivalued right-hand side and the theory of nonlinear boundary problems. The theorem about solvability of differential-operator inclusions with nonlinear not coercive mappings  – of pseudo-monotone type, for evolutionary variational inequalities – was first proved and Yu.A. Dubynskyi method for evolutionary variational inequalities with non-coercive maps was scientifically proved.

We obtain fundamental results of nonlinear analysis sections, which are components of a new discipline “System Mathematics”, which serves the application of mathematical methods to applied problems of system analysis.

The gained results can be applied to study more accurate mathematical models of new Physics, Geophysics, Geo-informatics, which allow phase transitions and unilateral restrictions and are described, in particular, with the help of non-linear boundary problems with partial derivatives, the main part of its differential operator is believed to be not coercive. In addition, the suggested approach enables to examine these systems constructively with the help of new high-precision algorithms for finding approximate solutions.

Some results have been already included in the training disciplines of Applied Mathematics, Information Technologies and Systems Analysis. The results of the research are published in about 10 publications.

Results of the research work are implemented in the educational process for teaching such subjects as “Elements of Nonlinear Analysis”.

Using the results of research work a monograph and 6 articles have been published,  a PhD thesis has been defended and the concluding part has been prepared for defense; 10 reports on conferences have been delivered, including 6 international conferences.

 

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