Existence theorem for a model of dryland vegetation

In this article, we consider the dryland vegetation model proposed by Gilad et al [6,7]. This model consists of three nonlinear parabolic partial differential equations, one of which is degenerate parabolic of the family of the porous media equation [3,7], and we prove the existence of its weak solutions. Our approach based on the classical Galerkin methods combines and makes use of techniques, parabolic regularization, truncation, maximum principle, compactness. We observe in this way various properties and regularity results of the solutions.