AACIMP 2011 Summer School. Science of Global Challenges stream. Lecture by Pavlo Kasyanov.

1. M.Z. Zgurovsky, P.O. Kasyanov,
A.V. Kapustyan, N.V. Zadoianchuk
Institute for Applied System Analysis – AACIMP 2011 – Aug 9, 2011

2. 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.

3. Differential-
Geophysical
Mathematical operator
process or model (PDE) equation or
field
inclusion
y:Ω τ,Τ R y: τ,Τ R
y ,t R,
t ,T

4. 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.

5. 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

6. 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.

7. Theory of Global and Trajectory
Attractors for Infinite-dimensional
Dynamical Systems

32. Nonlinearized viscoelastisy theory
Piesoelectrisity theory
Hydrodynamic problems
Nonlinear contact problems
Mathematical biology problems
Feedback control problems
Sustainable development problems
etc

34. zgur@zgurov.kiev.ua kasyanov@i.ua