Global Existence and Uniqueness of the Weak Solution in Thixotropic Model

Abstract

In this paper, we study global existence, uniqueness and boundedness of the weak solution for the system (P) which is formulated by two subsystems (P1) and (P2), the first describes the thixotropic problem and the second describes the diffusion degradation of c, using Galerkin’s method, Lax-Milgran’s and maximum principle. Moreover we show that the unique solution is positive.