Existence theorems for cooperative systems of parabolic PDEs and applications in chemistry

Abstract

One of the most important applications of comparison principle is the well known method of sub- and super-solutions, known as method of upper- and lower solutions as well. In this paper it is applied to the diffraction problem in bounded domain for cooperative system of quasi-linear parabolic PDE. The existence of upper and lower solutions is shown as well on a model example-reaction diffusion system arising in chemistry.