Study About Vegetation Patterns And Desertification Model

In this paper, we study the local existence and uniqueness of solutions of initialboundary value problem for a vegetation patterns and desertification model. Then weprove that the nonnegative constant and nonconstant steady solutions of the problem areasymptotically stable under some conditions.The whole paper consists of two chapters. In the first chapter, we introduce somebackground and the main results of this thesis brie?y. In chapter 2, we prove the localexistence and uniqueness of solutions for this model,then we study the stability andasymptotical stability of the nonnegative steady solution for the equations and get theattractive area of the nonnegative nonconstant steady solution.