Local boundedness for doubly degenerate quasi-linear parabolic systems

Abstract

We establish the local boundedness of weak solutions for the degenerate quasilinear parabolic systems ∂u i ∂t − ∑ j=1 n ∂ ∂x j |u| α ∂u ∂x p−2 ∂u i ∂x j =C|u| α−1 ∂u ∂x p−1 u i, i=1,…,N; N≥1 .