# American Institute of Mathematical Sciences

July  2011, 16(1): 197-224. doi: 10.3934/dcdsb.2011.16.197

## Existence theorem for a model of dryland vegetation

 1 18-20 Avenue De La République, 92400, Courbevoie, France 2 Laboratoire d'Analyse Numérique, Université Paris Sud, Orsay, France 3 Institute for Dryland Environmental Research, BIDR, Ben-Gurion University, Sede Boqer campus 84990, Israel 4 The Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, IN, 47205, United States

Received  June 2010 Revised  January 2011 Published  April 2011

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.
Citation: Yukie Goto, Danielle Hilhorst, Ehud Meron, Roger Temam. Existence theorem for a model of dryland vegetation. Discrete & Continuous Dynamical Systems - B, 2011, 16 (1) : 197-224. doi: 10.3934/dcdsb.2011.16.197
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