Existence theorem for a model of dryland vegetation

Yukie Goto, Danielle Hilhorst, Ehud Meron, Roger Temam

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)197-224
Number of pages28
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume16
Issue number1
DOIs
StatePublished - 1 Jul 2011

Keywords

  • Compactness theorems
  • Degenerate parabolic equations
  • Desertification
  • Dryland vegetation
  • Galerkin approximation
  • Parabolic equations
  • Porous media equations

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