The shift-semiflow of a multi-valued evolution equation from climate modeling

This note is concerned with a variant of the trajectory space approach ([3] , [4], [16]) which applies to reaction-diffusion problems with slow diffusi on and jump discontinuities in the source term. Such problems arise from Bu dyko-type energy balance climate models, and typically the initial value pr oblem for the resulting parabolic differential inclusion is not uniquely so lvable. It will be shown that the shift-semigroup on a suitable trajectory space, a complete subset of a Frechet space of continuous functions, posses ses a global compact attractor.