An energy balance climate model with hysteresis

Energy balance climate models of Budyko type lead to reaction–diffusion equations with slow diffusion and memory on the 2-sphere. The reaction part exhibits a jump discontinuity (at the snow line). Here we introduce a Babuška–Duhem hysteresis in order to account for a frequent repetition of sudden and fast warming followed by much slower cooling as observed from paleoclimate proxy data. Existence of global solutions and of a trajectory attractor will be established for the resulting system of a parabolic differential inclusion and an ode.