Lately due to intensification of investigation processes in economics, ecology, geophysics, synergy and geoinformatics there has been appeared the necessity for more detail studying of arising nonlinear effects, new classes of mathematical models with nonlinear, nonsmooth, discontinuos and multivalued dependence between determinative parameters of problem, control problems for nonlinear processes and fields, long-range forecast problems for state functions of solutions for such problems. We present fundamental research of such problems in the following directions:
- Multiple-purpose investigation of the methods of nonlinear and multivalued analysis (analysis of distributions of state functions, their long-time forecasts, pullback attractors);
- Investigations of classes of mathematical models of piesoelectric, climate models with nonlinear, discontinuous and multivalued interaction functions in the form of mathematically graunded results and high-precision algorithms for searching solutions as well as in the form of particular software products;
- Long-time forecastings for state functions of nonlinearized geophysical processes and fields, problems of viscoelastisity theory, hydrodynamisc, heat-and-mass transfer, piesoelectric, nonlinear contact problems, mathematical models of biology and medicine;
- Qualitative analysis of forecasting and stability problems of technology processes.
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Tutor of the course:
Prof. P. Kasyanov, Institute for Applied System Analysis, NTUU KPI, Ukraine