Time periodic solutions for a diffusive energy balance model in climatology

Abstract

We prove the existence of a periodic solution to the problem u(t) - Delta(p)u + R-e(x,u) is an element of mu Q(x,t)beta(u) in M x R, assumed p greater than or equal to 2, M a compact connected and oriented bidimensional Riemannian manifold without boundary, beta(u) a bounded maximal monotone graph (the coalbedo), Q(x, t) a time periodic function (the incoming solar radiation flux) and R-e a time independent strictly increasing function of the surface temperature u (the Earth emitted energy)