Periodic weak solutions for the quasi-linear parabolic chafee-infante equation by fixed point theorem

The authors of this manuscript have worked to investigate the existence of the time periodic weak solution Quasi-linear Chafee-Infante Equation with periodic initial conditions and Neumann boundary conditions. Since the equation our paper is degenerate, so we first need to establish the regular problem. By using Moser iteration technique, we establish a priori upper bound of the weak solution by using a good method that is called the Moser iteration technique. Then by usig the way of contradiction, we get a priori lower bound of the weak solution. This paper is based mainly on the fixed point theorem of infinite spaces, where we used the Leray–Schauder theory to investigate the existence of a non-trivial non-negative time periodic weak solution.