Time periodic solutions for a diffusive energy balance model in climatology (Q1290968)

The authors deal with the existence of periodic solutions of the nonlinear parabolic problem of the form: \(u_t-\Delta_p u+R_e(x,u) \in\mu Q(x,t) \beta(u)\) in \({\mathcal M}\times\mathbb{R}\), (1) where \(p\geq 2\), \({\mathcal M}\) is a compact connected and oriented bidimensional Riemannian manifold with \(\partial {\mathcal M}=\emptyset\). Here \(\Delta_p u=\text{div}(|\nabla u |^{p-2}|\nabla u|)\), \(\beta(u)\) a bounded maximal monotone graph, \(Q(x,t)\) a time periodic function. Since (1) belongs to the degenerate type of parabolic equations, the authors deal with the existence of (bounded) weak solutions using in particular cases super and subsolution techniques.