Periodic solutions for a Sellers type diffusive energy balance model in climatology (Q1589933)

The author deals with a one-dimensional degenerate reaction-diffusion equation of the form \[ u_t-k\bigl((1-x^2)|u_x|^{p-2}u_x\bigr)_x=R(x,t,u) \qquad\text{on }(-1,1)\times\mathbb{R}, \] which arises from an energy balance climate model if one neglects the spatial dependence of the heat inertia term and the diffusivity. \noindent He establishes the unique solvability of the initial value problem and the existence of a maximal and minimal periodic solution (assuming that the incoming solar radiation flux is periodic). The proof of the latter relies on sub- and supersolutions, Poincaré map, Schauder's fixed point theorem and successive approximation. The corresponding two-dimensional model (two-sphere rather than \([-1,1]\)) has been investigated by the author and \textit{J. I. Díaz} [J. Math. Anal. Appl. 233, 713-729 (1999; Zbl 0933.37071)].