Global existence and asymptotic behavior for a quasilinear reaction-diffusion system from climate modeling

Abstract

This paper is concerned with a weakly coupled system of quasilinear autonomous strongly parabolic equations on a compact two-dimensional manifold without boundary; the system arises from an energy balance climate model. We establish L ∞, Hoelder, and Sobolev estimates, and apply general results on quasilinear evolution equations in order to guarantee the existence of classical nonnegative solutions. More precisely, it is shown that the system generates a global solution semiflow in the positive cone of some fractional order Sobolev space. Employing elements of the theory of infinite-dimensional dissipative systems, we prove the existence of a connected global attractor. Finally, we present some results about stationary solutions and forced periodic oscillations. The present paper extends earlier work of the authors on a semilinear problem.