Post on 20-Jun-2015
description
M.Z. Zgurovsky, P.O. Kasyanov,
A.V. Kapustyan, N.V. Zadoianchuk
Institute for Applied System Analysis – AACIMP 2011 – Aug 9, 2011
The concentric circles represent
the disciplinary research needed
in the social, natural, health
and engineering sciences and
the humanities that must be
carried out alongside
interdisciplinary and
transdisciplinary research in
order to address the challenges.
The lines linking the grand
challenges show that progress in
addressing any challenge will
require progress in addressing
each of the others.
Earth System Science for Global Sustainability: The Grand
Challenges. International Council for Science, Paris.
Geophysical process or
field
Mathematical model (PDE)
Differential-operator
equation or inclusion
Rτ,Τy:Ω
Tt
Rty
Rτ,Τy:
,
,,
studying of new classes of energetic extensions and Nemitsky operators for differential operators from initial mathematical models;
structure investigations of corresponding phase and extended phase spaces;
proving of new embedding and approximation theorems for special classes of distribution spaces, basis theorems for such spaces;
generalization of Ky Fan theorem for multistrategies;
development of noncorrosive theory for differential operator inclusions with pseudomonotone type maps.
Research Laboratory of Nonlinear Analysis for Differential-Operator Systems of Institute for Applied System Analysis of NAS of Ukraine carries out fundamental investigations of such problems in the following directions
http://iasa.kpi.ua
nonlinear analysis and control for classes of nonlinear geophysics processes and fields;
properties of solutions of differential-operator inclusions and multivariation inequalities for Earth data analysis problems;
theory of global and trajectory attractors for infinite-dimensional dynamical systems.
Theory of Global and Trajectory Attractors for Infinite-dimensional Dynamical Systems
Nonlinearized viscoelastisy theory
Piesoelectrisity theory
Hydrodynamic problems
Nonlinear contact problems
Mathematical biology problems
Feedback control problems
Sustainable development problems
etc