Global Existence and Uniqueness of the Weak Solution in Keller Segel Model

Abstract

This paper deals with the global existence, uniqueness and boundedness of the weak solution for the chemotaxis system (P) defined as The system (P) is under homogeneous Dirichlet boundary conditions in a convex smooth bounded domain with smooth boundary Based on method, Lax -Milgran’s and maximum principle, a prove of the existence and uniqueness of a global solution for the system (P) is determined. Moreover we show that the unique solution is positive.