On the mathematical analysis of the limit case of a radiative—convective climate model

Abstract

We study the limit case corresponding to a model introduced by G.L. Stenchikov and A. Robock for the evolution of the temperature of an atmospheric column in absence of humidity. The model envolves a degenerate noncoercive quasilinear equation. The diffusion coefficient depends of the atmospheric stability and vanishes on the stable regions. We show the existence and uniqueness of a suitable class of weak solutions and prove that the number of stable and unstable regions are nonincreasing in time.