On the exact number of monotone solutions of a simplifed Budyko climate model and their different stability

2018/08/12 by Sabri Bensid, Bensid, Sabri, Jesús Ildefonso Díaz Díaz +1 · 1 citation
Engineering · Medicine · Earth and Planetary Sciences · #Stability and Controllability of Differential Equations #Mathematical and Theoretical Epidemiology and Ecology Models #Arctic and Antarctic ice dynamics

paper · pdf · doi:10.48550/arxiv.1808.03979

Abstract

We consider a simplified version of the Budyko diffusive energy balance climate model. We obtain the exact number of monotone stationary solutions of the associated discontinuous nonlinear elliptic with absorption. We show that the bifurcation curve, in terms of the solar constant parameter, is S-shaped. We prove the instability of the decreasing part and the stability of the increasing part of the bifurcation curve. In terms of the Budyko climate problem the above results lead to an important qualitative information which is far to be evident and which seems to be new in the mathematical literature on climate models. We prove that if the solar constant is represented by λ∈ (λ₁,λ₂), for suitable λ₁

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