Global weak solution to a generic reaction-diffusion nonlinear parabolic system

In this study, we proof the existence of global weak solution for a new generic reaction-diffusion system. It is in fact a generalization of the work presented in 2014, 2016 and 2018. In the first, we truncate the system, and by using Schauder fixed point theorem in Banach spaces, we show the existence of a solution for this approached problem. Finally, by making some estimations, we prove that the solution of the truncated equation converges to the solution of our problem.