Qualitative properties and finite-dimensionality up to a small parameter of weak solutions for the Budyko–Sellers climate model

Authors

  • Michael Z. Zgurovsky National technical university of Ukraine "Igor Sikorsky Kyiv polytechnic institute", Kyiv, Ukraine https://orcid.org/0000-0001-5896-7466
  • Pavlo O. Kasyanov Educational and scientific complex "Institute for applied system analysis" of the National technical university of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine https://orcid.org/0000-0002-6662-0160
  • Nataliia V. Gorban The Institute for applied system analysis of the National technical university of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine https://orcid.org/0000-0003-3517-8549
  • Liliia S. Paliichuk The Institute for applied system analysis of the National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine https://orcid.org/0000-0003-1654-4371

DOI:

https://doi.org/10.20535/SRIT.2308-8893.2018.4.01

Keywords:

energy balance climate model, global attractor, trajectory attractor, finite-dimensionality up to a small parameter, multi-valued semi-flow, weak solution

Abstract

A qualitative analysis of the solutions behavior for the Budyko–Sellers energy balance climate model, considered on the Riemannian manifold without the boundary, is carried out. The global existence of the weak solution for the investigated problem with arbitrary initial data from the phase space is established. Solutions properties and regularity are studied. The Lyapunov function is found. 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 studied. The relationship between attractors and the space of complete trajectories of 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 for the problem is established.

Author Biographies

Michael Z. Zgurovsky, National technical university of Ukraine "Igor Sikorsky Kyiv polytechnic institute", Kyiv

Michael Zakharovych Zgurovsky,

Academician of the National Academy of Sciences of Ukraine, Doctor of Technical Sciences, Professor, Rector of National technical university of Ukraine "Igor Sikorsky Kyiv polytechnic institute", Kyiv, Ukraine.

Pavlo O. Kasyanov, Educational and scientific complex "Institute for applied system analysis" of the National technical university of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv

Kasyanov Pavlo Olegovych,

Doctor of Physical and Mathematical Sciences, Director of Educational and scientific complex "Institute for applied system analysis" of the National technical university of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine.

Nataliia V. Gorban, The Institute for applied system analysis of the National technical university of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv

Gorban Nataliia Volodymyrivna,

Candidate of Physical and Mathematical Sciences (Ph.D.), an associate professor at the Department of Mathematical methods of System Analysis of the Institute for applied system analysis of the National technical university of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine.

Liliia S. Paliichuk, The Institute for applied system analysis of the National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv

Liliia Serhiivna Paliichuk,

Candidate of Physical and Mathematical Sciences (Ph.D.), an assistant at the Department of Mathematical methods of System Analysis of the Institute for applied system analysis of the National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine.

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Published

2018-12-18

Issue

Section

Theoretical and applied problems and methods of system analysis