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Cybernetics And Systems Analysis
International Theoretical Science Journal
UDC 517.9
M.Z. Zgurovsky1, P.O Kasyanov2, N.V. Gorban3, L.S. Paliichuk4


1 National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute,” Kyiv, Ukraine

zgurovsm@hotmail.com; mzz@kpi.ua

2 Educational-scientific complex “Institute for applied system analysis” of the National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute,” Kyiv, Ukraine

p.o.kasyanov@gmail.com

3 Educational-scientific complex “Institute for applied system analysis” of the National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute,” Kyiv, Ukraine

nataliia.v.gorban@gmail.com

4 Educational-scientific complex “Institute for applied system analysis” of the National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute,” Kyiv, Ukraine

lili262808@gmail.com

QUALITATIVE AND QUANTITATIVE ANALYSIS OF WEAK SOLUTIONS
OF ENERGY-BALANCE CLIMATOLOGICAL MODELS

Abstract. A qualitative analysis of the solutions behavior for the Budyko–Sellers energy balance climate model, considered on the Riemannian manifold without boundary is carried out. The global existence of the weak solution for the investigated problem with arbitrary initial data from the phase space is proved. Solutions’ properties and regularity are analyzed. The theorems on the existence of global and trajectory attractors for multi-valued semi-flow generated by all weak solutions of the problem are proved. The properties of attractors are analyzed. The relationship between attractors and the space of complete trajectories for the problem is established. The character of attraction of solutions to global and trajectory attractors and their structure are investigated. The finite-dimensionality up to a small parameter of the solutions dynamics is obtained.

Keywords: Budyko–Sellers energy balance climate model, global attractor, trajectory attractor, finite-dimensionality up to a small parameter, multi-valued semi-flow, weak solution, reaction–diffusion equation.



FULL TEXT

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