Degenerate and singular parabolic systems

Abstract

We turn now to quasilinear systems whose principal part becomes either degenerate or singular at points where. To present a streamlined cross section of the theory, we refer to the model system

$$ \left\{{\begin{array}{*{20}{c}} {u \equiv \left( {{u_1},{u_2}, \ldots,{u_m}} \right),m\in N,}\\ {{u_i}\in{C_{loc}}\left({0,T;L_{loc}^2\left(\Omega\right)}\right)\cap {L^p}\left({0,T;W_{loc}^{1,p}\left(\Omega \right)} \right),i=1,2,\ldots,m,}\\ {{u_t}- div{{\left| {Du}\right|}^{p - 2}}Du =0in{\Omega_{\rm T}}} \end{array}}\right. $$

(1.1)