Steady-State Solutions of a Diffusive Energy-Balance Climate Model and Their Stability
NEW YORK UNIV NY COURANT INST OF MATHEMATICAL SCIENCES
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A diffusive energy-balance climate model is considered, governed by a nonlinear parabolic partial differential equation. Three positive steady-state solutions of this equation are found they correspond to three possible climates of our planet an interglacial nearly identical to the present climate, a glacial, and a completely ice-covered earth. Also considered are models similar to the main one studied, and the number of their steady states are determined. All the models have albedo continuously varying with latitude and temperature, and entirely diffusive horizontal heat transfer. The diffusion is taken to be nonlinear as well as linear. The stability under small perturbations of the main models climates are investigated. A stability criterion is derived, and its application shows that the present climate and the deep freeze are stable, whereas the models glacial is unstable.