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Qualitative and Quantitative Analysis of Weak Solutions of Energy-Balance Climate Models

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Abstract

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 semiflow 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.

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Authors and Affiliations

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

    M. Z. Zgurovsky

  2. Educational and Scientific Complex “Institute of Applied Systems Analysis” of the National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine

    P. O Kasyanov, N. V. Gorban & L. S. Paliichuk

Authors
  1. M. Z. Zgurovsky
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  2. P. O Kasyanov
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  3. N. V. Gorban
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  4. L. S. Paliichuk
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Correspondence to M. Z. Zgurovsky.

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Translated from Kibernetika i Sistemnyi Analiz, No. 4, July–August, 2019, pp. 39–49.

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Zgurovsky, M.Z., Kasyanov, P.O., Gorban, N.V. et al. Qualitative and Quantitative Analysis of Weak Solutions of Energy-Balance Climate Models. Cybern Syst Anal 55, 552–560 (2019). https://doi.org/10.1007/s10559-019-00164-1

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  • DOI: https://doi.org/10.1007/s10559-019-00164-1

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