On the existence of weak solutions of nonlinear degenerate parabolic system with variable exponents

The main goal of the present paper is establishing the existence and uniqueness of weak solutions for the nonlinear degenerate reaction-diffusion system with variable exponents. A model also is proposed to characterize the invasion of cancer cells towards healthy cells with acidification environment. Moreover, the main results of this paper are obtained using regularization problem, the Faedo-Galerkin approximation method, some apriori estimates, compactness results and the Gronwall Lemma.