Methods of Nonlinear and Multivalued Analysis for Multinature Controlled Processes and Fields
M.Z. Zgurovsky, P.O. Kasyanov,A.V. Kapustyan, N.V. ZadoianchukInstitute for Applied System Analysis – AACIMP 2011 – Aug 9, 2011
The concentric circles representthe disciplinary research neededin the social, natural, healthand engineering sciences andthe humanities that must becarried out alongsideinterdisciplinary andtransdisciplinary research inorder to address the challenges.The lines linking the grandchallenges show that progress inaddressing any challenge willrequire progress in addressingeach of the others.Earth System Science for Global Sustainability: The GrandChallenges. International Council for Science, Paris.
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
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 forDifferential-Operator Systems of Institute forApplied System Analysis of NAS of Ukrainecarries out fundamental investigations of suchproblems 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 TrajectoryAttractors for Infinite-dimensionalDynamical Systems
Nonlinearized viscoelastisy theoryPiesoelectrisity theoryHydrodynamic problemsNonlinear contact problemsMathematical biology problemsFeedback control problemsSustainable development problemsetc