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

## 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.## References

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