Abstract: This paper deals with the equation:
∂β(u)+▽[vβ(u)-▽u]=f in D'(Q_T) where Q_T=Ω×(0,T], Ω is a bounded domain with piecewise smooth boundary, β is maximal monotone graph,v:Q_T→R^m There are weak solutions to the evloutionary and seady-state problems associated with this equation, provided the boundary conditions on u are chosen appropriately. We also prove the uniqueness of both problems.